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netgen/libsrc/meshing/curvedelems.cpp
Joachim Schoeberl 9b3578740f a hex has 12 edges, doesn't it?
2021-09-09 11:49:48 +02:00

4771 lines
126 KiB
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#include <mystdlib.h>
#include "meshing.hpp"
#include "../general/autodiff.hpp"
namespace netgen
{
// bool rational = true;
static void ComputeGaussRule (int n, NgArray<double> & xi, NgArray<double> & wi)
{
xi.SetSize (n);
wi.SetSize (n);
int m = (n+1)/2;
double p1, p2, p3;
double pp, z, z1;
for (int i = 1; i <= m; i++)
{
z = cos ( M_PI * (i - 0.25) / (n + 0.5));
while(1)
{
p1 = 1; p2 = 0;
for (int j = 1; j <= n; j++)
{
p3 = p2; p2 = p1;
p1 = ((2 * j - 1) * z * p2 - (j - 1) * p3) / j;
}
// p1 is legendre polynomial
pp = n * (z*p1-p2) / (z*z - 1);
z1 = z;
z = z1-p1/pp;
if (fabs (z - z1) < 1e-14) break;
}
xi[i-1] = 0.5 * (1 - z);
xi[n-i] = 0.5 * (1 + z);
wi[i-1] = wi[n-i] = 1.0 / ( (1 - z * z) * pp * pp);
}
}
// compute edge bubbles up to order n, x \in (-1, 1)
template <typename T>
static void CalcEdgeShape (int n, T x, T * shape)
{
T p1 = x, p2 = -1, p3 = 0;
for (int j=2; j<=n; j++)
{
p3=p2; p2=p1;
p1=( (2*j-3) * x * p2 - (j-3) * p3) / j;
shape[j-2] = p1;
}
}
template <typename T, typename FUNC>
static void CalcEdgeShapeLambda (int n, T x, FUNC func)
{
T p1(x), p2(-1.0), p3(0.0);
for (int j=2; j<=n; j++)
{
p3=p2; p2=p1;
p1=( (2*j-3) * x * p2 - (j-3) * p3) / j;
func(j-2, p1);
}
}
template <typename T>
static void CalcEdgeDx (int n, T x, T * dshape)
{
T p1 = x, p2 = -1, p3 = 0;
T p1dx = 1, p2dx = 0, p3dx = 0;
for (int j=2; j<=n; j++)
{
p3=p2; p2=p1;
p3dx = p2dx; p2dx = p1dx;
p1=( (2*j-3) * x * p2 - (j-3) * p3) / j;
p1dx = ( (2*j-3) * (x * p2dx + p2) - (j-3) * p3dx) / j;
dshape[j-2] = p1dx;
}
}
template <typename T>
static void CalcEdgeShapeDx (int n, T x, T * shape, T * dshape)
{
T p1 = x, p2 = -1, p3 = 0;
T p1dx = 1, p2dx = 0, p3dx = 0;
for (int j=2; j<=n; j++)
{
p3=p2; p2=p1;
p3dx = p2dx; p2dx = p1dx;
p1=( (2*j-3) * x * p2 - (j-3) * p3) / j;
p1dx = ( (2*j-3) * (x * p2dx + p2) - (j-3) * p3dx) / j;
shape[j-2] = p1;
dshape[j-2] = p1dx;
}
}
// compute L_i(x/t) * t^i
template <typename T>
static void CalcScaledEdgeShape (int n, T x, T t, T * shape)
{
static bool init = false;
static double coefs[100][2];
if (!init)
{
for (int j = 0; j < 100; j++)
{
coefs[j][0] = double(2*j+1)/(j+2);
coefs[j][1] = -double(j-1)/(j+2);
}
init = true;
}
T p1 = x, p2 = -1, p3 = 0;
T tt = t*t;
for (int j=0; j<=n-2; j++)
{
p3=p2; p2=p1;
p1= coefs[j][0] * x * p2 + coefs[j][1] * tt*p3;
// p1=( (2*j+1) * x * p2 - t*t*(j-1) * p3) / (j+2);
shape[j] = p1;
}
}
template <typename T, typename FUNC>
static void CalcScaledEdgeShapeLambda (int n, T x, T t, FUNC func)
{
static bool init = false;
static double coefs[100][2];
if (!init)
{
for (int j = 0; j < 100; j++)
{
coefs[j][0] = double(2*j+1)/(j+2);
coefs[j][1] = -double(j-1)/(j+2);
}
init = true;
}
T p1(x), p2(-1.0), p3(0.0);
T tt = t*t;
for (int j=0; j<=n-2; j++)
{
p3=p2; p2=p1;
p1= coefs[j][0] * x * p2 + coefs[j][1] * tt*p3;
// p1=( (2*j+1) * x * p2 - t*t*(j-1) * p3) / (j+2);
func(j, p1);
}
}
template <int DIST, typename T>
static void CalcScaledEdgeShapeDxDt (int n, T x, T t, T * dshape)
{
T p1 = x, p2 = -1, p3 = 0;
T p1dx = 1, p1dt = 0;
T p2dx = 0, p2dt = 0;
T p3dx = 0, p3dt = 0;
for (int j=0; j<=n-2; j++)
{
p3=p2; p3dx=p2dx; p3dt = p2dt;
p2=p1; p2dx=p1dx; p2dt = p1dt;
p1 = ( (2*j+1) * x * p2 - t*t*(j-1) * p3) / (j+2);
p1dx = ( (2*j+1) * (x * p2dx + p2) - t*t*(j-1) * p3dx) / (j+2);
p1dt = ( (2*j+1) * x * p2dt - (j-1)* (t*t*p3dt+2*t*p3)) / (j+2);
// shape[j] = p1;
dshape[DIST*j ] = p1dx;
dshape[DIST*j+1] = p1dt;
}
}
template <class Tx, class Tres>
static void LegendrePolynomial (int n, Tx x, Tres * values)
{
switch (n)
{
case 0:
values[0] = 1;
break;
case 1:
values[0] = 1;
values[1] = x;
break;
default:
if (n < 0) return;
Tx p1 = 1.0, p2 = 0.0, p3;
values[0] = 1.0;
for (int j=1; j<=n; j++)
{
p3 = p2; p2 = p1;
p1 = ((2.0*j-1.0)*x*p2 - (j-1.0)*p3) / j;
values[j] = p1;
}
}
}
template <class Tx, class Tt, class Tres>
static void ScaledLegendrePolynomial (int n, Tx x, Tt t, Tres * values)
{
switch (n)
{
case 0:
values[0] = 1.0;
break;
case 1:
values[0] = 1.0;
values[1] = x;
break;
default:
if (n < 0) return;
Tx p1 = 1.0, p2 = 0.0, p3;
values[0] = 1.0;
for (int j=1; j<=n; j++)
{
p3 = p2; p2 = p1;
p1 = ((2.0*j-1.0)*x*p2 - t*t*(j-1.0)*p3) / j;
values[j] = p1;
}
}
}
class RecPol
{
protected:
int maxorder;
double *a, *b, *c;
public:
RecPol (int amaxorder)
{
maxorder = amaxorder;
a = new double[maxorder+1];
b = new double[maxorder+1];
c = new double[maxorder+1];
}
~RecPol ()
{
delete [] a;
delete [] b;
delete [] c;
}
template <class S, class T>
void Evaluate (int n, S x, T * values)
{
S p1(1.0), p2(0.0), p3;
if (n >= 0)
p2 = values[0] = 1.0;
if (n >= 1)
p1 = values[1] = a[0]+b[0]*x;
for (int i = 1; i < n; i++)
{
p3 = p2; p2=p1;
p1 = (a[i]+b[i]*x)*p2-c[i]*p3;
values[i+1] = p1;
}
}
template <class S, class T>
void EvaluateScaled (int n, S x, S y, T * values)
{
S p1(1.0), p2(0.0), p3;
if (n >= 0)
p2 = values[0] = 1.0;
if (n >= 1)
p1 = values[1] = a[0]*y+b[0]*x;
for (int i = 1; i < n; i++)
{
p3 = p2; p2=p1;
p1 = (a[i]*y+b[i]*x)*p2-c[i]*y*y*p3;
values[i+1] = p1;
}
}
template <class S, class FUNC>
void EvaluateScaledLambda (int n, S x, S y, FUNC func)
{
S p1(1.0), p2(0.0), p3;
if (n >= 0)
{
p2 = 1.0;
func(0, p2);
}
if (n >= 1)
{
p1 = a[0]*y+b[0]*x;
func(1, p1);
}
for (int i = 1; i < n; i++)
{
p3 = p2; p2=p1;
p1 = (a[i]*y+b[i]*x)*p2-c[i]*y*y*p3;
func(i+1, p1);
}
}
};
class JacobiRecPol : public RecPol
{
public:
JacobiRecPol (int amo, double al, double be)
: RecPol (amo)
{
for (int i = 0; i <= maxorder; i++)
{
double den = 2*(i+1)*(i+al+be+1)*(2*i+al+be);
a[i] = (2*i+al+be+1)*(al*al-be*be) / den;
b[i] = (2*i+al+be)*(2*i+al+be+1)*(2*i+al+be+2) / den;
c[i] = 2*(i+al)*(i+be)*(2*i+al+be+2) / den;
}
}
};
template <class S, class T>
inline void JacobiPolynomial (int n, S x, double alpha, double beta, T * values)
{
S p1 = 1.0, p2 = 0.0, p3;
if (n >= 0)
p2 = values[0] = 1.0;
if (n >= 1)
p1 = values[1] = 0.5 * (2*(alpha+1)+(alpha+beta+2)*(x-1));
for (int i = 1; i < n; i++)
{
p3 = p2; p2=p1;
p1 =
1.0 / ( 2 * (i+1) * (i+alpha+beta+1) * (2*i+alpha+beta) ) *
(
( (2*i+alpha+beta+1)*(alpha*alpha-beta*beta) +
(2*i+alpha+beta)*(2*i+alpha+beta+1)*(2*i+alpha+beta+2) * x)
* p2
- 2*(i+alpha)*(i+beta) * (2*i+alpha+beta+2) * p3
);
values[i+1] = p1;
}
}
template <class S, class St, class T>
inline void ScaledJacobiPolynomial (int n, S x, St t, double alpha, double beta, T * values)
{
/*
S p1 = 1.0, p2 = 0.0, p3;
if (n >= 0) values[0] = 1.0;
*/
S p1(1.0), p2(0.0), p3;
if (n >= 0)
p2 = values[0] = 1.0;
if (n >= 1)
p1 = values[1] = 0.5 * (2*(alpha+1)*t+(alpha+beta+2)*(x-t));
for (int i=1; i < n; i++)
{
p3 = p2; p2=p1;
p1 =
1.0 / ( 2 * (i+1) * (i+alpha+beta+1) * (2*i+alpha+beta) ) *
(
( (2*i+alpha+beta+1)*(alpha*alpha-beta*beta) * t +
(2*i+alpha+beta)*(2*i+alpha+beta+1)*(2*i+alpha+beta+2) * x)
* p2
- 2*(i+alpha)*(i+beta) * (2*i+alpha+beta+2) * t * t * p3
);
values[i+1] = p1;
}
}
static NgArray<shared_ptr<RecPol>> jacpols2;
void CurvedElements::buildJacPols()
{
if (!jacpols2.Size())
{
jacpols2.SetSize (100);
for (int i = 0; i < 100; i++)
jacpols2[i] = make_shared<JacobiRecPol> (100, i, 2);
}
}
// compute face bubbles up to order n, 0 < y, y-x < 1, x+y < 1
template <class Tx, class Ty, class Ts>
static void CalcTrigShape (int n, Tx x, Ty y, Ts * shape)
{
// cout << "calc trig shape" << endl;
if (n < 3) return;
Tx hx[50], hy[50*50];
jacpols2[2] -> EvaluateScaled (n-3, x, 1-y, hx);
for (int ix = 0; ix <= n-3; ix++)
jacpols2[2*ix+5] -> Evaluate (n-3, 2*y-1, hy+50*ix);
int ii = 0;
Tx bub = (1+x-y)*y*(1-x-y);
for (int ix = 0; ix <= n-3; ix++)
hx[ix] *= bub;
/*
for (int iy = 0; iy <= n-3; iy++)
for (int ix = 0; ix <= n-3-iy; ix++)
shape[ii++] = hx[ix]*hy[iy+50*ix];
*/
// change loops:
for (int ix = 0; ix <= n-3; ix++)
for (int iy = 0; iy <= n-3-ix; iy++)
shape[ii++] = hx[ix]*hy[iy+50*ix];
}
template <typename T>
static void CalcTrigShapeDxDy (int n, T x, T y, T * dshape)
{
if (n < 3) return;
AutoDiff<2,T> adx(x, 0);
AutoDiff<2,T> ady(y, 1);
AutoDiff<2,T> res[2000];
CalcTrigShape (n, adx, ady, &res[0]);
int ndof = (n-1)*(n-2)/2;
for (int i = 0; i < ndof; i++)
{
dshape[2*i] = res[i].DValue(0);
dshape[2*i+1] = res[i].DValue(1);
}
}
// compute face bubbles up to order n, 0 < y, y-x < 1, x+y < 1
template <class Tx, class Ty, class Tt, class Tr>
static void CalcScaledTrigShape (int n, Tx x, Ty y, Tt t, Tr * shape)
{
if (n < 3) return;
Tx hx[50], hy[50];
ScaledJacobiPolynomial (n-3, x, t-y, 2, 2, hx);
int ii = 0;
Tx bub = (t+x-y)*y*(t-x-y);
for (int ix = 0; ix <= n-3; ix++)
{
jacpols2[2*ix+5] -> EvaluateScaled (n-3, 2*y-1, t, hy);
for (int iy = 0; iy <= n-3-ix; iy++)
shape[ii++] = bub * hx[ix]*hy[iy];
}
}
template <class Tx, class Ty, class Tt, typename FUNC>
static void CalcScaledTrigShapeLambda (int n, Tx x, Ty y, Tt t, FUNC func)
{
if (n < 3) return;
int ii = 0;
Tx bub = (t+x-y)*y*(t-x-y);
jacpols2[2]->EvaluateScaledLambda
(n-3, x, t-y,
[&](int ix, Tx valx)
{
jacpols2[2*ix+5] -> EvaluateScaledLambda (n-3-ix, 2*y-1, t, [&](int iy, Ty valy)
{
func(ii++, bub*valx*valy);
});
});
}
// compute face bubbles up to order n, 0 < y, y-x < 1, x+y < 1
template <typename T>
static void CalcScaledTrigShapeDxDyDt (int n, T x, T y, T t, T * dshape)
{
/*
if (n < 3) return;
AutoDiff<3,T> adx(x, 0);
AutoDiff<3,T> ady(y, 1);
AutoDiff<3,T> adt(t, 2);
AutoDiff<3,T> res[2000];
CalcScaledTrigShape (n, adx, ady, adt, &res[0]);
int ndof = (n-1)*(n-2)/2;
for (int i = 0; i < ndof; i++)
{
dshape[3*i] = res[i].DValue(0);
dshape[3*i+1] = res[i].DValue(1);
dshape[3*i+2] = res[i].DValue(2);
}
*/
if (n < 3) return;
AutoDiff<3,T> adx(x, 0);
AutoDiff<3,T> ady(y, 1);
AutoDiff<3,T> adt(t, 2);
CalcScaledTrigShapeLambda (n, adx, ady, adt,
[&] (int i, AutoDiff<3,T> shape)
{
dshape[3*i] = shape.DValue(0);
dshape[3*i+1] = shape.DValue(1);
dshape[3*i+2] = shape.DValue(2);
});
}
CurvedElements :: CurvedElements (const Mesh & amesh)
: mesh(amesh)
{
order = 1;
rational = 0;
ishighorder = 0;
}
CurvedElements :: ~CurvedElements()
{
}
void CurvedElements :: BuildCurvedElements(const Refinement * ref, int aorder,
bool arational)
{
auto & geo = *mesh.GetGeometry();
ishighorder = 0;
order = 1;
auto comm = mesh.GetCommunicator();
#ifdef PARALLEL
enum { MPI_TAG_CURVE = MPI_TAG_MESH+20 };
const ParallelMeshTopology & partop = mesh.GetParallelTopology ();
#endif
int ntasks = comm.Size();
bool working = (ntasks == 1) || (comm.Rank() > 0);
if (working)
order = aorder;
if (mesh.coarsemesh)
{
mesh.coarsemesh->GetCurvedElements().BuildCurvedElements (ref, aorder, arational);
order = aorder;
rational = arational;
ishighorder = (order > 1);
return;
}
PrintMessage (1, "Curve elements, order = ", aorder);
if (rational) PrintMessage (1, "curved elements with rational splines");
// if (working)
const_cast<Mesh&> (mesh).UpdateTopology();
const MeshTopology & top = mesh.GetTopology();
rational = arational;
NgArray<int> edgenrs;
int nedges = top.GetNEdges();
int nfaces = top.GetNFaces();
edgeorder.SetSize (nedges);
faceorder.SetSize (nfaces);
edgeorder = 1;
faceorder = 1;
if (rational)
{
edgeweight.SetSize (nedges);
edgeweight = 1.0;
}
if (aorder <= 1)
{
for (ElementIndex ei = 0; ei < mesh.GetNE(); ei++)
if (mesh[ei].GetType() == TET10)
ishighorder = 1;
return;
}
if (rational) aorder = 2;
if (working)
{
if (mesh.GetDimension() == 3)
for (SurfaceElementIndex i = 0; i < mesh.GetNSE(); i++)
{
top.GetEdges (i, edgenrs);
for (int j = 0; j < edgenrs.Size(); j++)
edgeorder[edgenrs[j]] = aorder;
faceorder[top.GetFace (i)] = aorder;
}
for (SegmentIndex i = 0; i < mesh.GetNSeg(); i++)
edgeorder[top.GetEdge (i)] = aorder;
}
if (rational)
{
edgeorder = 2;
faceorder = 1;
}
#ifdef PARALLEL
TABLE<int> send_orders(ntasks), recv_orders(ntasks);
if (ntasks > 1 && working)
{
for (int e = 0; e < edgeorder.Size(); e++)
for (int proc : partop.GetDistantEdgeProcs(e))
send_orders.Add (proc, edgeorder[e]);
for (int f = 0; f < faceorder.Size(); f++)
for (int proc : partop.GetDistantFaceProcs(f))
send_orders.Add (proc, faceorder[f]);
}
if (ntasks > 1)
MyMPI_ExchangeTable (send_orders, recv_orders, MPI_TAG_CURVE, comm);
if (ntasks > 1 && working)
{
NgArray<int> cnt(ntasks);
cnt = 0;
for (int e = 0; e < edgeorder.Size(); e++)
for (auto proc : partop.GetDistantEdgeProcs(e))
edgeorder[e] = max(edgeorder[e], recv_orders[proc][cnt[proc]++]);
for (int f = 0; f < faceorder.Size(); f++)
for (auto proc : partop.GetDistantFaceProcs(f))
faceorder[f] = max(faceorder[f], recv_orders[proc][cnt[proc]++]);
}
#endif
edgecoeffsindex.SetSize (nedges+1);
int nd = 0;
for (int i = 0; i < nedges; i++)
{
edgecoeffsindex[i] = nd;
nd += max (0, edgeorder[i]-1);
}
edgecoeffsindex[nedges] = nd;
edgecoeffs.SetSize (nd);
edgecoeffs = Vec<3> (0,0,0);
facecoeffsindex.SetSize (nfaces+1);
nd = 0;
for (int i = 0; i < nfaces; i++)
{
facecoeffsindex[i] = nd;
if (top.GetFaceType(i+1) == TRIG)
nd += max2 (0, (faceorder[i]-1)*(faceorder[i]-2)/2);
else
nd += max2 (0, sqr(faceorder[i]-1));
}
facecoeffsindex[nfaces] = nd;
facecoeffs.SetSize (nd);
facecoeffs = Vec<3> (0,0,0);
if (!ref || aorder <= 1)
{
order = aorder;
return;
}
NgArray<double> xi, weight;
ComputeGaussRule (aorder+4, xi, weight); // on (0,1)
buildJacPols();
PrintMessage (3, "Curving edges");
if (mesh.GetDimension() == 3 || rational)
{
static Timer tce("curve edges"); RegionTimer reg(tce);
NgArray<int> surfnr(nedges);
NgArray<PointGeomInfo> gi0(nedges);
NgArray<PointGeomInfo> gi1(nedges);
surfnr = -1;
if (working)
for (SurfaceElementIndex i = 0; i < mesh.GetNSE(); i++)
{
top.GetEdges (i, edgenrs);
const Element2d & el = mesh[i];
const ELEMENT_EDGE * edges = MeshTopology::GetEdges0 (el.GetType());
for (int i2 = 0; i2 < edgenrs.Size(); i2++)
{
auto enr = edgenrs[i2];
surfnr[enr] = mesh.GetFaceDescriptor(el.GetIndex()).SurfNr();
if (el[edges[i2][0]] < el[edges[i2][1]])
{
gi0[enr] = el.GeomInfoPi(edges[i2][0]+1);
gi1[enr] = el.GeomInfoPi(edges[i2][1]+1);
}
else
{
gi1[enr] = el.GeomInfoPi(edges[i2][0]+1);
gi0[enr] = el.GeomInfoPi(edges[i2][1]+1);
}
}
}
#ifdef PARALLEL
if (ntasks > 1)
{
// distribute it ...
TABLE<double> senddata(ntasks), recvdata(ntasks);
if (working)
for (int e = 0; e < nedges; e++)
for (int proc : partop.GetDistantEdgeProcs(e))
{
senddata.Add (proc, surfnr[e]);
if (surfnr[e] != -1)
{
senddata.Add (proc, gi0[e].trignum);
senddata.Add (proc, gi0[e].u);
senddata.Add (proc, gi0[e].v);
senddata.Add (proc, gi1[e].trignum);
senddata.Add (proc, gi1[e].u);
senddata.Add (proc, gi1[e].v);
}
}
MyMPI_ExchangeTable (senddata, recvdata, MPI_TAG_CURVE, comm);
NgArray<int> cnt(ntasks);
cnt = 0;
if (working)
for (int e = 0; e < nedges; e++)
for (int proc : partop.GetDistantEdgeProcs(e))
{
int surfnr1 = recvdata[proc][cnt[proc]++];
if (surfnr1 != -1)
{
surfnr[e] = surfnr1;
gi0[e].trignum = int (recvdata[proc][cnt[proc]++]);
gi0[e].u = recvdata[proc][cnt[proc]++];
gi0[e].v = recvdata[proc][cnt[proc]++];
gi1[e].trignum = int (recvdata[proc][cnt[proc]++]);
gi1[e].u = recvdata[proc][cnt[proc]++];
gi1[e].v = recvdata[proc][cnt[proc]++];
}
}
}
#endif
if (working)
for (int e = 0; e < surfnr.Size(); e++)
{
if (surfnr[e] == -1) continue;
SetThreadPercent(double(e)/surfnr.Size()*100.);
PointIndex pi1, pi2;
top.GetEdgeVertices (e+1, pi1, pi2);
bool swap = (pi1 > pi2);
Point<3> p1 = mesh[pi1];
Point<3> p2 = mesh[pi2];
int order1 = edgeorder[e];
int ndof = max (0, order1-1);
if (rational && order1 >= 2)
{
Point<3> pm = Center (p1, p2);
Vec<3> n1 = geo.GetNormal (surfnr[e], p1, &gi0[e]);
Vec<3> n2 = geo.GetNormal (surfnr[e], p2, &gi1[e]);
// p3 = pm + alpha1 n1 + alpha2 n2
Mat<2> mat, inv;
Vec<2> rhs, sol;
mat(0,0) = n1*n1;
mat(0,1) = mat(1,0) = n1*n2;
mat(1,1) = n2*n2;
rhs(0) = n1 * (p1-pm);
rhs(1) = n2 * (p2-pm);
Point<3> p3;
if (fabs (Det (mat)) > 1e-10)
{
CalcInverse (mat, inv);
sol = inv * rhs;
p3 = pm + sol(0) * n1 + sol(1) * n2;
}
else
p3 = pm;
edgecoeffs[edgecoeffsindex[e]] = Vec<3> (p3);
double wold = 1, w = 1, dw = 0.1;
double dold = 1e99;
while (fabs (dw) > 1e-12)
{
Vec<3> v05 = 0.25 * Vec<3> (p1) + 0.5*w* Vec<3>(p3) + 0.25 * Vec<3> (p2);
v05 /= 1 + (w-1) * 0.5;
Point<3> p05 (v05), pp05(v05);
geo.ProjectPointGI(surfnr[e], pp05, gi0[e]);
double d = Dist (pp05, p05);
if (d < dold)
{
dold = d;
wold = w;
w += dw;
}
else
{
dw *= -0.7;
w = wold + dw;
}
}
edgeweight[e] = w;
continue;
}
Vector shape(ndof);
DenseMatrix mat(ndof, ndof), inv(ndof, ndof),
rhs(ndof, 3), sol(ndof, 3);
rhs = 0.0;
mat = 0.0;
for (int j = 0; j < xi.Size(); j++)
{
Point<3> p;
Point<3> pp;
PointGeomInfo ppgi;
if (swap)
{
p = p1 + xi[j] * (p2-p1);
geo.PointBetween (p1, p2, xi[j],
surfnr[e], gi0[e], gi1[e],
pp, ppgi);
}
else
{
p = p2 + xi[j] * (p1-p2);
geo.PointBetween (p2, p1, xi[j],
surfnr[e], gi1[e], gi0[e],
pp, ppgi);
}
Vec<3> dist = pp - p;
CalcEdgeShape (order1, 2*xi[j]-1, &shape(0));
for (int k = 0; k < ndof; k++)
for (int l = 0; l < ndof; l++)
mat(k,l) += weight[j] * shape(k) * shape(l);
for (int k = 0; k < ndof; k++)
for (int l = 0; l < 3; l++)
rhs(k,l) += weight[j] * shape(k) * dist(l);
}
CalcInverse (mat, inv);
Mult (inv, rhs, sol);
int first = edgecoeffsindex[e];
for (int j = 0; j < ndof; j++)
for (int k = 0; k < 3; k++)
edgecoeffs[first+j](k) = sol(j,k);
}
}
NgArray<int> use_edge(nedges);
NgArray<int> edge_surfnr1(nedges);
NgArray<int> edge_surfnr2(nedges);
NgArray<int> swap_edge(nedges);
NgArray<EdgePointGeomInfo> edge_gi0(nedges);
NgArray<EdgePointGeomInfo> edge_gi1(nedges);
use_edge = 0;
if (working)
for (SegmentIndex i = 0; i < mesh.GetNSeg(); i++)
{
const Segment & seg = mesh[i];
int edgenr = top.GetEdge (i);
use_edge[edgenr] = 1;
edge_surfnr1[edgenr] = seg.surfnr1;
edge_surfnr2[edgenr] = seg.surfnr2;
edge_gi0[edgenr] = seg.epgeominfo[0];
edge_gi1[edgenr] = seg.epgeominfo[1];
swap_edge[edgenr] = int (seg[0] > seg[1]);
}
#ifdef PARALLEL
if (ntasks > 1)
{
// distribute it ...
TABLE<double> senddata(ntasks), recvdata(ntasks);
if (working)
for (int e = 0; e < nedges; e++)
for (int proc : partop.GetDistantEdgeProcs(e))
{
senddata.Add (proc, use_edge[e]);
if (use_edge[e])
{
senddata.Add (proc, edge_surfnr1[e]);
senddata.Add (proc, edge_surfnr2[e]);
senddata.Add (proc, edge_gi0[e].edgenr);
senddata.Add (proc, edge_gi0[e].body);
senddata.Add (proc, edge_gi0[e].dist);
senddata.Add (proc, edge_gi0[e].u);
senddata.Add (proc, edge_gi0[e].v);
senddata.Add (proc, edge_gi1[e].edgenr);
senddata.Add (proc, edge_gi1[e].body);
senddata.Add (proc, edge_gi1[e].dist);
senddata.Add (proc, edge_gi1[e].u);
senddata.Add (proc, edge_gi1[e].v);
senddata.Add (proc, swap_edge[e]);
}
}
MyMPI_ExchangeTable (senddata, recvdata, MPI_TAG_CURVE, comm);
NgArray<int> cnt(ntasks);
cnt = 0;
if (working)
for (int e = 0; e < edge_surfnr1.Size(); e++)
for (int proc : partop.GetDistantEdgeProcs(e))
{
int get_edge = int(recvdata[proc][cnt[proc]++]);
if (get_edge)
{
use_edge[e] = 1;
edge_surfnr1[e] = int (recvdata[proc][cnt[proc]++]);
edge_surfnr2[e] = int (recvdata[proc][cnt[proc]++]);
edge_gi0[e].edgenr = int (recvdata[proc][cnt[proc]++]);
edge_gi0[e].body = int (recvdata[proc][cnt[proc]++]);
edge_gi0[e].dist = recvdata[proc][cnt[proc]++];
edge_gi0[e].u = recvdata[proc][cnt[proc]++];
edge_gi0[e].v = recvdata[proc][cnt[proc]++];
edge_gi1[e].edgenr = int (recvdata[proc][cnt[proc]++]);
edge_gi1[e].body = int (recvdata[proc][cnt[proc]++]);
edge_gi1[e].dist = recvdata[proc][cnt[proc]++];
edge_gi1[e].u = recvdata[proc][cnt[proc]++];
edge_gi1[e].v = recvdata[proc][cnt[proc]++];
swap_edge[e] = recvdata[proc][cnt[proc]++];
}
}
}
#endif
if (working)
for (int edgenr = 0; edgenr < use_edge.Size(); edgenr++)
{
int segnr = edgenr;
if (!use_edge[edgenr]) continue;
SetThreadPercent(double(edgenr)/edge_surfnr1.Size()*100.);
PointIndex pi1, pi2;
top.GetEdgeVertices (edgenr+1, pi1, pi2);
bool swap = swap_edge[edgenr]; // (pi1 > pi2);
if (swap) Swap (pi1, pi2);
Point<3> p1 = mesh[pi1];
Point<3> p2 = mesh[pi2];
int order1 = edgeorder[segnr];
int ndof = max (0, order1-1);
if (rational)
{
Vec<3> tau1 = geo.GetTangent(p1, edge_surfnr2[edgenr], edge_surfnr1[edgenr],
edge_gi0[edgenr]);
Vec<3> tau2 = geo.GetTangent(p2, edge_surfnr2[edgenr], edge_surfnr1[edgenr],
edge_gi1[edgenr]);
// p1 + alpha1 tau1 = p2 + alpha2 tau2;
Mat<3,2> mat;
Mat<2,3> inv;
Vec<3> rhs;
Vec<2> sol;
for (int j = 0; j < 3; j++)
{
mat(j,0) = tau1(j);
mat(j,1) = -tau2(j);
rhs(j) = p2(j)-p1(j);
}
CalcInverse (mat, inv);
sol = inv * rhs;
Point<3> p3 = p1+sol(0) * tau1;
edgecoeffs[edgecoeffsindex[segnr]] = Vec<3> (p3);
double wold = 1, w = 1, dw = 0.1;
double dold = 1e99;
while (fabs (dw) > 1e-12)
{
Vec<3> v05 = 0.25 * Vec<3> (p1) + 0.5*w* Vec<3>(p3) + 0.25 * Vec<3> (p2);
v05 /= 1 + (w-1) * 0.5;
Point<3> p05 (v05), pp05(v05);
geo.ProjectPointEdge(edge_surfnr1[edgenr], edge_surfnr2[edgenr], pp05,
&edge_gi0[edgenr]);
double d = Dist (pp05, p05);
if (d < dold)
{
dold = d;
wold = w;
w += dw;
}
else
{
dw *= -0.7;
w = wold + dw;
}
// *testout << "w = " << w << ", dw = " << dw << endl;
}
// cout << "wopt = " << w << ", dopt = " << dold << endl;
edgeweight[segnr] = w;
// cout << "p1 = " << p1 << ", tau1 = " << tau1 << ", alpha1 = " << sol(0) << endl;
// cout << "p2 = " << p2 << ", tau2 = " << tau2 << ", alpha2 = " << -sol(1) << endl;
// cout << "p+alpha tau = " << p1 + sol(0) * tau1
// << " =?= " << p2 +sol(1) * tau2 << endl;
}
else
{
Vector shape(ndof);
DenseMatrix mat(ndof, ndof), inv(ndof, ndof),
rhs(ndof, 3), sol(ndof, 3);
rhs = 0.0;
mat = 0.0;
for (int j = 0; j < xi.Size(); j++)
{
Point<3> p, pp;
EdgePointGeomInfo ppgi;
if (swap)
{
p = p1 + xi[j] * (p2-p1);
geo.PointBetweenEdge(p1, p2, xi[j],
edge_surfnr2[edgenr], edge_surfnr1[edgenr],
edge_gi0[edgenr], edge_gi1[edgenr],
pp, ppgi);
}
else
{
p = p2 + xi[j] * (p1-p2);
geo.PointBetweenEdge(p2, p1, xi[j],
edge_surfnr2[edgenr], edge_surfnr1[edgenr],
edge_gi1[edgenr], edge_gi0[edgenr],
pp, ppgi);
}
Vec<3> dist = pp - p;
CalcEdgeShape (order1, 2*xi[j]-1, &shape(0));
for (int k = 0; k < ndof; k++)
for (int l = 0; l < ndof; l++)
mat(k,l) += weight[j] * shape(k) * shape(l);
for (int k = 0; k < ndof; k++)
for (int l = 0; l < 3; l++)
rhs(k,l) += weight[j] * shape(k) * dist(l);
}
CalcInverse (mat, inv);
Mult (inv, rhs, sol);
int first = edgecoeffsindex[segnr];
for (int j = 0; j < ndof; j++)
for (int k = 0; k < 3; k++)
edgecoeffs[first+j](k) = sol(j,k);
}
}
PrintMessage (3, "Curving faces");
NgArray<int> surfnr(nfaces);
surfnr = -1;
if (working)
for (SurfaceElementIndex i = 0; i < mesh.GetNSE(); i++)
surfnr[top.GetFace(i)] =
mesh.GetFaceDescriptor(mesh[i].GetIndex()).SurfNr();
#ifdef PARALLEL
TABLE<int> send_surfnr(ntasks), recv_surfnr(ntasks);
if (ntasks > 1 && working)
{
for (int f = 0; f < nfaces; f++)
for (int proc : partop.GetDistantFaceProcs(f))
send_surfnr.Add (proc, surfnr[f]);
}
if (ntasks > 1)
MyMPI_ExchangeTable (send_surfnr, recv_surfnr, MPI_TAG_CURVE, comm);
if (ntasks > 1 && working)
{
NgArray<int> cnt(ntasks);
cnt = 0;
for (int f = 0; f < nfaces; f++)
for (int proc : partop.GetDistantFaceProcs(f))
surfnr[f] = max(surfnr[f], recv_surfnr[proc][cnt[proc]++]);
}
#endif
if (mesh.GetDimension() == 3 && working)
{
static Timer tcf("curve faces"); RegionTimer reg(tcf);
for (int f = 0; f < nfaces; f++)
{
int facenr = f;
if (surfnr[f] == -1) continue;
// if (el.GetType() == TRIG && order >= 3)
if (top.GetFaceType(facenr+1) == TRIG && order >= 3)
{
NgArrayMem<int, 3> verts(3);
top.GetFaceVertices (facenr+1, verts);
int fnums[] = { 0, 1, 2 };
/*
if (el[fnums[0]] > el[fnums[1]]) swap (fnums[0], fnums[1]);
if (el[fnums[1]] > el[fnums[2]]) swap (fnums[1], fnums[2]);
if (el[fnums[0]] > el[fnums[1]]) swap (fnums[0], fnums[1]);
*/
if (verts[fnums[0]] > verts[fnums[1]]) swap (fnums[0], fnums[1]);
if (verts[fnums[1]] > verts[fnums[2]]) swap (fnums[1], fnums[2]);
if (verts[fnums[0]] > verts[fnums[1]]) swap (fnums[0], fnums[1]);
int order1 = faceorder[facenr];
int ndof = max (0, (order1-1)*(order1-2)/2);
Vector shape(ndof), dmat(ndof);
MatrixFixWidth<3> rhs(ndof), sol(ndof);
rhs = 0.0;
dmat = 0.0;
int np = sqr(xi.Size());
NgArray<Point<2> > xia(np);
NgArray<Point<3> > xa(np);
for (int jx = 0, jj = 0; jx < xi.Size(); jx++)
for (int jy = 0; jy < xi.Size(); jy++, jj++)
xia[jj] = Point<2> ((1-xi[jy])*xi[jx], xi[jy]);
// CalcMultiPointSurfaceTransformation (&xia, i, &xa, NULL);
NgArray<int> edgenrs;
top.GetFaceEdges (facenr+1, edgenrs);
for (int k = 0; k < edgenrs.Size(); k++) edgenrs[k]--;
for (int jj = 0; jj < np; jj++)
{
Point<3> pp(0,0,0);
double lami[] = { xia[jj](0), xia[jj](1), 1-xia[jj](0)-xia[jj](1)};
for (int k = 0; k < verts.Size(); k++)
pp += lami[k] * Vec<3> (mesh.Point(verts[k]));
// const ELEMENT_EDGE * edges = MeshTopology::GetEdges0 (TRIG);
for (int k = 0; k < edgenrs.Size(); k++)
{
int eorder = edgeorder[edgenrs[k]];
if (eorder < 2) continue;
int first = edgecoeffsindex[edgenrs[k]];
Vector eshape(eorder-1);
int vi1, vi2;
top.GetEdgeVertices (edgenrs[k]+1, vi1, vi2);
if (vi1 > vi2) swap (vi1, vi2);
int v1 = -1, v2 = -1;
for (int j = 0; j < 3; j++)
{
if (verts[j] == vi1) v1 = j;
if (verts[j] == vi2) v2 = j;
}
CalcScaledEdgeShape (eorder, lami[v1]-lami[v2], lami[v1]+lami[v2], &eshape(0));
for (int n = 0; n < eshape.Size(); n++)
pp += eshape(n) * edgecoeffs[first+n];
}
xa[jj] = pp;
}
for (int jx = 0, jj = 0; jx < xi.Size(); jx++)
for (int jy = 0; jy < xi.Size(); jy++, jj++)
{
double y = xi[jy];
double x = (1-y) * xi[jx];
double lami[] = { x, y, 1-x-y };
double wi = weight[jx]*weight[jy]*(1-y);
Point<3> pp = xa[jj];
// ref -> ProjectToSurface (pp, mesh.GetFaceDescriptor(el.GetIndex()).SurfNr());
/**
with MPI and an interior surface element between volume elements assigned to different
procs, only one of them has the surf-el
**/
SurfaceElementIndex sei = top.GetFace2SurfaceElement (f+1)-1;
if (sei != SurfaceElementIndex(-1)) {
PointGeomInfo gi = mesh[sei].GeomInfoPi(1);
// use improved initial guess
gi.u = (lami[fnums[0]]*mesh[sei].GeomInfoPi(1).u+lami[fnums[1]]*mesh[sei].GeomInfoPi(2).u+lami[fnums[2]]*mesh[sei].GeomInfoPi(3).u);
gi.v = (lami[fnums[0]]*mesh[sei].GeomInfoPi(1).v+lami[fnums[1]]*mesh[sei].GeomInfoPi(2).v+lami[fnums[2]]*mesh[sei].GeomInfoPi(3).v);
geo.ProjectPointGI(surfnr[facenr], pp, gi);
}
else
{ geo.ProjectPoint(surfnr[facenr], pp); }
Vec<3> dist = pp-xa[jj];
CalcTrigShape (order1, lami[fnums[1]]-lami[fnums[0]],
1-lami[fnums[1]]-lami[fnums[0]], &shape(0));
for (int k = 0; k < ndof; k++)
dmat(k) += wi * shape(k) * shape(k);
dist *= wi;
for (int k = 0; k < ndof; k++)
for (int l = 0; l < 3; l++)
rhs(k,l) += shape(k) * dist(l);
}
for (int i = 0; i < ndof; i++)
for (int j = 0; j < 3; j++)
sol(i,j) = rhs(i,j) / dmat(i); // Orthogonal basis !
int first = facecoeffsindex[facenr];
for (int j = 0; j < ndof; j++)
for (int k = 0; k < 3; k++)
facecoeffs[first+j](k) = sol(j,k);
}
}
}
// compress edge and face tables
int newbase = 0;
for (int i = 0; i < edgeorder.Size(); i++)
{
bool curved = 0;
int oldbase = edgecoeffsindex[i];
int nd = edgecoeffsindex[i+1] - edgecoeffsindex[i];
for (int j = 0; j < nd; j++)
if (edgecoeffs[oldbase+j].Length() > 1e-12)
curved = 1;
if (rational) curved = 1;
if (curved && newbase != oldbase)
for (int j = 0; j < nd; j++)
edgecoeffs[newbase+j] = edgecoeffs[oldbase+j];
edgecoeffsindex[i] = newbase;
if (!curved) edgeorder[i] = 1;
if (curved) newbase += nd;
}
edgecoeffsindex.Last() = newbase;
newbase = 0;
for (int i = 0; i < faceorder.Size(); i++)
{
bool curved = 0;
int oldbase = facecoeffsindex[i];
int nd = facecoeffsindex[i+1] - facecoeffsindex[i];
for (int j = 0; j < nd; j++)
if (facecoeffs[oldbase+j].Length() > 1e-12)
curved = 1;
if (curved && newbase != oldbase)
for (int j = 0; j < nd; j++)
facecoeffs[newbase+j] = facecoeffs[oldbase+j];
facecoeffsindex[i] = newbase;
if (!curved) faceorder[i] = 1;
if (curved) newbase += nd;
}
facecoeffsindex.Last() = newbase;
if (working)
ishighorder = (order > 1);
// (*testout) << "edgecoeffs = " << endl << edgecoeffs << endl;
// (*testout) << "facecoeffs = " << endl << facecoeffs << endl;
#ifdef PARALLEL
comm.Barrier();
#endif
}
// *********************** Transform edges *****************************
bool CurvedElements :: IsSegmentCurved (SegmentIndex elnr) const
{
if (mesh.coarsemesh)
{
const HPRefElement & hpref_el =
(*mesh.hpelements) [mesh[elnr].hp_elnr];
return mesh.coarsemesh->GetCurvedElements().IsSegmentCurved (hpref_el.coarse_elnr);
}
SegmentInfo info;
info.elnr = elnr;
info.order = order;
info.ndof = info.nv = 2;
if (info.order > 1)
{
const MeshTopology & top = mesh.GetTopology();
info.edgenr = top.GetSegmentEdge (elnr+1)-1;
info.ndof += edgeorder[info.edgenr]-1;
}
return (info.ndof > info.nv);
}
template <typename T>
void CurvedElements ::
CalcSegmentTransformation (const T & xi, SegmentIndex elnr,
Point<3,T> * x, Vec<3,T> * dxdxi, bool * curved)
{
if (mesh.coarsemesh)
{
const HPRefElement & hpref_el =
(*mesh.hpelements) [mesh[elnr].hp_elnr];
// xi umrechnen
T lami[2] = { xi, 1-xi };
T dlami[2] = { 1, -1 };
T coarse_xi = 0;
T trans = 0;
for (int i = 0; i < 2; i++)
{
coarse_xi += hpref_el.param[i][0] * lami[i];
trans += hpref_el.param[i][0] * dlami[i];
}
mesh.coarsemesh->GetCurvedElements().CalcSegmentTransformation (coarse_xi, hpref_el.coarse_elnr, x, dxdxi, curved);
if (dxdxi) *dxdxi *= trans;
return;
}
// TVector<T> shapes, dshapes;
// NgArray<Vec<3> > coefs;
SegmentInfo info;
info.elnr = elnr;
info.order = order;
info.ndof = info.nv = 2;
if (info.order > 1)
{
const MeshTopology & top = mesh.GetTopology();
info.edgenr = top.GetSegmentEdge (elnr+1)-1;
info.ndof += edgeorder[info.edgenr]-1;
}
NgArrayMem<Vec<3>,100> coefs(info.ndof);
NgArrayMem<T, 100> shapes_mem(info.ndof);
TFlatVector<T> shapes(info.ndof, &shapes_mem[0]);
NgArrayMem<T, 200> dshapes_mem(info.ndof);
TFlatVector<T> dshapes(info.ndof, &dshapes_mem[0]);
CalcElementShapes (info, xi, shapes);
GetCoefficients (info, coefs);
*x = 0;
for (int i = 0; i < shapes.Size(); i++)
// *x += shapes(i) * coefs[i];
for (int j = 0; j < 3; j++)
(*x)(j) += shapes(i) * coefs[i](j);
if (dxdxi)
{
CalcElementDShapes (info, xi, dshapes);
*dxdxi = 0;
for (int i = 0; i < shapes.Size(); i++)
for (int j = 0; j < 3; j++)
(*dxdxi)(j) += dshapes(i) * coefs[i](j);
}
if (curved)
*curved = (info.order > 1);
// cout << "Segment, |x| = " << Abs2(Vec<3> (*x) ) << endl;
}
template <typename T>
void CurvedElements ::
CalcElementShapes (SegmentInfo & info, T xi, TFlatVector<T> shapes) const
{
/*
if (rational && info.order == 2)
{
shapes.SetSize(3);
double w = edgeweight[info.edgenr];
shapes(0) = xi*xi;
shapes(1) = (1-xi)*(1-xi);
shapes(2) = 2*w*xi*(1-xi);
shapes *= 1.0 / (1 + (w-1) *2*xi*(1-xi));
return;
}
*/
// shapes.SetSize(info.ndof);
shapes(0) = xi;
shapes(1) = 1-xi;
if (info.order >= 2)
{
if (mesh[info.elnr][0] > mesh[info.elnr][1])
xi = 1-xi;
CalcEdgeShape (edgeorder[info.edgenr], 2*xi-1, &shapes(2));
}
}
template <typename T>
void CurvedElements ::
CalcElementDShapes (SegmentInfo & info, T xi, TFlatVector<T> dshapes) const
{
/*
if (rational && info.order == 2)
{
dshapes.SetSize(3);
double wi = edgeweight[info.edgenr];
double shapes[3];
shapes[0] = xi*xi;
shapes[1] = (1-xi)*(1-xi);
shapes[2] = 2*wi*xi*(1-xi);
double w = 1 + (wi-1) *2*xi*(1-xi);
double dw = (wi-1) * (2 - 4*xi);
dshapes(0) = 2*xi;
dshapes(1) = 2*(xi-1);
dshapes(2) = 2*wi*(1-2*xi);
for (int j = 0;j < 3; j++)
dshapes(j) = dshapes(j) / w - shapes[j] * dw / (w*w);
return;
}
*/
// dshapes.SetSize(info.ndof);
dshapes = 0;
dshapes(0) = 1;
dshapes(1) = -1;
// int order = edgeorder[info.edgenr];
if (info.order >= 2)
{
T fac = 2;
if (mesh[info.elnr][0] > mesh[info.elnr][1])
{
xi = 1-xi;
fac *= -1;
}
CalcEdgeDx (edgeorder[info.edgenr], 2*xi-1, &dshapes(2));
for (int i = 2; i < dshapes.Size(); i++)
dshapes(i) *= fac;
}
// ??? not implemented ????
}
void CurvedElements ::
GetCoefficients (SegmentInfo & info, NgArray<Vec<3> > & coefs) const
{
const Segment & el = mesh[info.elnr];
coefs.SetSize(info.ndof);
coefs[0] = Vec<3> (mesh[el[0]]);
coefs[1] = Vec<3> (mesh[el[1]]);
if (info.order >= 2)
{
int first = edgecoeffsindex[info.edgenr];
int next = edgecoeffsindex[info.edgenr+1];
for (int i = 0; i < next-first; i++)
coefs[i+2] = edgecoeffs[first+i];
}
}
// ********************** Transform surface elements *******************
bool CurvedElements :: IsSurfaceElementCurved (SurfaceElementIndex elnr) const
{
if (mesh[elnr].GetType() != TRIG) return true;
if (!IsHighOrder()) return false;
if (mesh.coarsemesh)
{
const HPRefElement & hpref_el =
(*mesh.hpelements) [mesh[elnr].hp_elnr];
return mesh.coarsemesh->GetCurvedElements().IsSurfaceElementCurved (hpref_el.coarse_elnr);
}
const Element2d & el = mesh[elnr];
ELEMENT_TYPE type = el.GetType();
SurfaceElementInfo info;
info.elnr = elnr;
info.order = order;
switch (type)
{
case TRIG : info.nv = 3; break;
case QUAD : info.nv = 4; break;
case TRIG6: return true;
default:
cerr << "undef element in CalcSurfaceTrafo" << endl;
}
info.ndof = info.nv;
// info.ndof = info.nv = ( (type == TRIG) || (type == TRIG6) ) ? 3 : 4;
if (info.order > 1)
{
const MeshTopology & top = mesh.GetTopology();
top.GetSurfaceElementEdges (elnr+1, info.edgenrs);
for (int i = 0; i < info.edgenrs.Size(); i++)
info.edgenrs[i]--;
info.facenr = top.GetSurfaceElementFace (elnr+1)-1;
for (int i = 0; i < info.edgenrs.Size(); i++)
info.ndof += edgecoeffsindex[info.edgenrs[i]+1] - edgecoeffsindex[info.edgenrs[i]];
info.ndof += facecoeffsindex[info.facenr+1] - facecoeffsindex[info.facenr];
}
return (info.ndof > info.nv);
}
void CurvedElements ::
CalcSurfaceTransformation (Point<2> xi, SurfaceElementIndex elnr,
Point<3> * x, Mat<3,2> * dxdxi, bool * curved)
{
if (mesh.coarsemesh)
{
const HPRefElement & hpref_el =
(*mesh.hpelements) [mesh[elnr].hp_elnr];
// xi umrechnen
double lami[4];
FlatVector vlami(4, lami);
vlami = 0;
mesh[elnr].GetShapeNew (xi, vlami);
Mat<2,2> trans;
Mat<3,2> dxdxic;
if (dxdxi)
{
MatrixFixWidth<2> dlami(4);
dlami = 0;
mesh[elnr].GetDShapeNew (xi, dlami);
trans = 0;
for (int k = 0; k < 2; k++)
for (int l = 0; l < 2; l++)
for (int i = 0; i < hpref_el.np; i++)
trans(l,k) += hpref_el.param[i][l] * dlami(i, k);
}
Point<2> coarse_xi(0,0);
for (int i = 0; i < hpref_el.np; i++)
for (int j = 0; j < 2; j++)
coarse_xi(j) += hpref_el.param[i][j] * lami[i];
mesh.coarsemesh->GetCurvedElements().CalcSurfaceTransformation (coarse_xi, hpref_el.coarse_elnr, x, &dxdxic, curved);
if (dxdxi)
*dxdxi = dxdxic * trans;
return;
}
const Element2d & el = mesh[elnr];
ELEMENT_TYPE type = el.GetType();
SurfaceElementInfo info;
info.elnr = elnr;
info.order = order;
switch (type)
{
case TRIG : info.nv = 3; break;
case QUAD : info.nv = 4; break;
case TRIG6: info.nv = 6; break;
case QUAD8 : info.nv = 8; break;
default:
cerr << "undef element in CalcSurfaceTrafo" << endl;
}
info.ndof = info.nv;
if (info.order > 1)
{
const MeshTopology & top = mesh.GetTopology();
top.GetSurfaceElementEdges (elnr+1, info.edgenrs);
for (int i = 0; i < info.edgenrs.Size(); i++)
info.edgenrs[i]--;
info.facenr = top.GetSurfaceElementFace (elnr+1)-1;
bool firsttry = true;
bool problem = false;
while(firsttry || problem)
{
problem = false;
for (int i = 0; !problem && i < info.edgenrs.Size(); i++)
{
if(info.edgenrs[i]+1 >= edgecoeffsindex.Size())
problem = true;
else
info.ndof += edgecoeffsindex[info.edgenrs[i]+1] - edgecoeffsindex[info.edgenrs[i]];
}
if(info.facenr+1 >= facecoeffsindex.Size())
problem = true;
else
info.ndof += facecoeffsindex[info.facenr+1] - facecoeffsindex[info.facenr];
if(problem && !firsttry)
throw NgException("something wrong with curved elements");
if(problem)
BuildCurvedElements(NULL,order,rational);
firsttry = false;
}
}
Point<2> _xi(xi);
Point<3> _x;
Mat<3,2> _dxdxi;
if (EvaluateMapping (info, _xi, _x, _dxdxi))
{
if (x) *x = _x;
if (dxdxi) *dxdxi = _dxdxi;
return;
}
NgArrayMem<Vec<3>,100> coefs(info.ndof);
NgArrayMem<double, 100> shapes_mem(info.ndof);
TFlatVector<double> shapes(info.ndof, &shapes_mem[0]);
NgArrayMem<double, 200> dshapes_mem(2*info.ndof);
MatrixFixWidth<2> dshapes(info.ndof, &dshapes_mem[0]);
CalcElementShapes (info, xi, shapes);
GetCoefficients (info, coefs);
*x = 0;
for (int i = 0; i < coefs.Size(); i++)
*x += shapes(i) * coefs[i];
if (dxdxi)
{
CalcElementDShapes (info, xi, dshapes);
*dxdxi = 0;
for (int i = 0; i < coefs.Size(); i++)
for (int j = 0; j < 3; j++)
for (int k = 0; k < 2; k++)
(*dxdxi)(j,k) += dshapes(i,k) * coefs[i](j);
}
if (curved)
*curved = (info.ndof > info.nv);
}
template <typename T>
void CurvedElements ::
CalcElementShapes (SurfaceElementInfo & info, const Point<2,T> xi, TFlatVector<T> shapes) const
{
const Element2d & el = mesh[info.elnr];
// shapes.SetSize(info.ndof);
if (rational && info.order >= 2)
{
// shapes.SetSize(6);
T w(1);
T lami[3] = { xi(0), xi(1), 1-xi(0)-xi(1) };
for (int j = 0; j < 3; j++)
shapes(j) = lami[j] * lami[j];
const ELEMENT_EDGE * edges = MeshTopology::GetEdges1 (TRIG);
for (int j = 0; j < 3; j++)
{
T wi = edgeweight[info.edgenrs[j]];
shapes(j+3) = 2 * wi * lami[edges[j][0]-1] * lami[edges[j][1]-1];
w += (wi-1) * 2 * lami[edges[j][0]-1] * lami[edges[j][1]-1];
}
shapes *= 1.0 / w;
return;
}
switch (el.GetType())
{
case TRIG:
{
shapes(0) = xi(0);
shapes(1) = xi(1);
shapes(2) = 1-xi(0)-xi(1);
if (info.order == 1) return;
int ii = 3;
const ELEMENT_EDGE * edges = MeshTopology::GetEdges0 (TRIG);
for (int i = 0; i < 3; i++)
{
int eorder = edgeorder[info.edgenrs[i]];
if (eorder >= 2)
{
int vi1 = edges[i][0], vi2 = edges[i][1];
if (el[vi1] > el[vi2]) swap (vi1, vi2);
CalcScaledEdgeShape (eorder, shapes(vi1)-shapes(vi2), shapes(vi1)+shapes(vi2), &shapes(ii));
ii += eorder-1;
}
}
int forder = faceorder[info.facenr];
if (forder >= 3)
{
int fnums[] = { 0, 1, 2 };
if (el[fnums[0]] > el[fnums[1]]) swap (fnums[0], fnums[1]);
if (el[fnums[1]] > el[fnums[2]]) swap (fnums[1], fnums[2]);
if (el[fnums[0]] > el[fnums[1]]) swap (fnums[0], fnums[1]);
CalcTrigShape (forder,
shapes(fnums[1])-shapes(fnums[0]),
1-shapes(fnums[1])-shapes(fnums[0]), &shapes(ii));
}
break;
}
case TRIG6:
{
if (shapes.Size() == 3)
{
shapes(0) = xi(0);
shapes(1) = xi(1);
shapes(2) = 1-xi(0)-xi(1);
}
else
{
T x = xi(0);
T y = xi(1);
T lam3 = 1-x-y;
shapes(0) = x * (2*x-1);
shapes(1) = y * (2*y-1);
shapes(2) = lam3 * (2*lam3-1);
shapes(3) = 4 * y * lam3;
shapes(4) = 4 * x * lam3;
shapes(5) = 4 * x * y;
}
break;
}
case QUAD:
{
shapes(0) = (1-xi(0))*(1-xi(1));
shapes(1) = xi(0) *(1-xi(1));
shapes(2) = xi(0) * xi(1) ;
shapes(3) = (1-xi(0))* xi(1) ;
if (info.order == 1) return;
T mu[4] = {
1 - xi(0) + 1 - xi(1),
xi(0) + 1 - xi(1),
xi(0) + xi(1),
1 - xi(0) + xi(1),
};
int ii = 4;
const ELEMENT_EDGE * edges = MeshTopology::GetEdges1 (QUAD);
for (int i = 0; i < 4; i++)
{
int eorder = edgeorder[info.edgenrs[i]];
if (eorder >= 2)
{
int vi1 = edges[i][0]-1, vi2 = edges[i][1]-1;
if (el[vi1] > el[vi2]) swap (vi1, vi2);
CalcEdgeShape (eorder, mu[vi1]-mu[vi2], &shapes(ii));
T lame = shapes(vi1)+shapes(vi2);
for (int j = 0; j < order-1; j++)
shapes(ii+j) *= lame;
ii += eorder-1;
}
}
for (int i = ii; i < info.ndof; i++)
shapes(i) = 0;
break;
}
case QUAD8:
{
auto x = xi(0), y = xi(1);
shapes(0) = (1-x)*(1-y);
shapes(1) = x*(1-y);
shapes(2) = x*y;
shapes(3) = (1-x)*y;
shapes(4) = 4*(1-x)*x*(1-y);
shapes(5) = 4*(1-x)*x*y;
shapes(6) = 4*(1-y)*y*(1-x);
shapes(7) = 4*(1-y)*y*x;
shapes(0) -= 0.5*(shapes(4)+shapes(6));
shapes(1) -= 0.5*(shapes(4)+shapes(7));
shapes(2) -= 0.5*(shapes(5)+shapes(7));
shapes(3) -= 0.5*(shapes(5)+shapes(6));
break;
}
default:
throw NgException("CurvedElements::CalcShape 2d, element type not handled");
};
}
template <typename T>
void CurvedElements ::
CalcElementDShapes (SurfaceElementInfo & info, const Point<2,T> xi, MatrixFixWidth<2,T> & dshapes) const
{
const Element2d & el = mesh[info.elnr];
ELEMENT_TYPE type = el.GetType();
T lami[4];
dshapes.SetSize(info.ndof);
// dshapes = 0;
// *testout << "calcelementdshapes, info.ndof = " << info.ndof << endl;
if (rational && info.order >= 2)
{
T w = 1;
T dw[2] = { 0, 0 };
lami[0] = xi(0); lami[1] = xi(1); lami[2] = 1-xi(0)-xi(1);
T dlami[3][2] = { { 1, 0 }, { 0, 1 }, { -1, -1 }};
T shapes[6];
for (int j = 0; j < 3; j++)
{
shapes[j] = lami[j] * lami[j];
dshapes(j,0) = 2 * lami[j] * dlami[j][0];
dshapes(j,1) = 2 * lami[j] * dlami[j][1];
}
const ELEMENT_EDGE * edges = MeshTopology::GetEdges1 (TRIG);
for (int j = 0; j < 3; j++)
{
T wi = edgeweight[info.edgenrs[j]];
shapes[j+3] = 2 * wi * lami[edges[j][0]-1] * lami[edges[j][1]-1];
for (int k = 0; k < 2; k++)
dshapes(j+3,k) = 2*wi* (lami[edges[j][0]-1] * dlami[edges[j][1]-1][k] +
lami[edges[j][1]-1] * dlami[edges[j][0]-1][k]);
w += (wi-1) * 2 * lami[edges[j][0]-1] * lami[edges[j][1]-1];
for (int k = 0; k < 2; k++)
dw[k] += 2*(wi-1) * (lami[edges[j][0]-1] * dlami[edges[j][1]-1][k] +
lami[edges[j][1]-1] * dlami[edges[j][0]-1][k]);
}
// shapes *= 1.0 / w;
dshapes *= 1.0 / w;
for (int i = 0; i < 6; i++)
for (int j = 0; j < 2; j++)
dshapes(i,j) -= shapes[i] * dw[j] / (w*w);
return;
}
switch (type)
{
case TRIG:
{
dshapes(0,0) = 1;
dshapes(0,1) = 0.0;
dshapes(1,0) = 0.0;
dshapes(1,1) = 1;
dshapes(2,0) = -1;
dshapes(2,1) = -1;
if (info.order == 1) return;
// *testout << "info.order = " << info.order << endl;
lami[0] = xi(0);
lami[1] = xi(1);
lami[2] = 1-xi(0)-xi(1);
int ii = 3;
const ELEMENT_EDGE * edges = MeshTopology::GetEdges1 (TRIG);
for (int i = 0; i < 3; i++)
{
int eorder = edgeorder[info.edgenrs[i]];
if (eorder >= 2)
{
int vi1 = edges[i][0]-1, vi2 = edges[i][1]-1;
if (el[vi1] > el[vi2]) swap (vi1, vi2);
CalcScaledEdgeShapeDxDt<2> (eorder, lami[vi1]-lami[vi2], lami[vi1]+lami[vi2], &dshapes(ii,0));
Mat<2,2,T> trans;
for (int j = 0; j < 2; j++)
{
trans(0,j) = dshapes(vi1,j)-dshapes(vi2,j);
trans(1,j) = dshapes(vi1,j)+dshapes(vi2,j);
}
for (int j = 0; j < eorder-1; j++)
{
T ddx = dshapes(ii+j,0);
T ddt = dshapes(ii+j,1);
dshapes(ii+j,0) = ddx * trans(0,0) + ddt * trans(1,0);
dshapes(ii+j,1) = ddx * trans(0,1) + ddt * trans(1,1);
}
ii += eorder-1;
}
}
int forder = faceorder[info.facenr];
// *testout << "forder = " << forder << endl;
if (forder >= 3)
{
int fnums[] = { 0, 1, 2 };
if (el[fnums[0]] > el[fnums[1]]) swap (fnums[0], fnums[1]);
if (el[fnums[1]] > el[fnums[2]]) swap (fnums[1], fnums[2]);
if (el[fnums[0]] > el[fnums[1]]) swap (fnums[0], fnums[1]);
CalcTrigShapeDxDy (forder,
lami[fnums[1]]-lami[fnums[0]],
1-lami[fnums[1]]-lami[fnums[0]], &dshapes(ii,0));
int nd = (forder-1)*(forder-2)/2;
Mat<2,2,T> trans;
for (int j = 0; j < 2; j++)
{
trans(0,j) = dshapes(fnums[1],j)-dshapes(fnums[0],j);
trans(1,j) = -dshapes(fnums[1],j)-dshapes(fnums[0],j);
}
for (int j = 0; j < nd; j++)
{
T ddx = dshapes(ii+j,0);
T ddt = dshapes(ii+j,1);
dshapes(ii+j,0) = ddx * trans(0,0) + ddt * trans(1,0);
dshapes(ii+j,1) = ddx * trans(0,1) + ddt * trans(1,1);
}
}
break;
}
case TRIG6:
{
if (dshapes.Height() == 3)
{
dshapes = T(0.0);
dshapes(0,0) = 1;
dshapes(1,1) = 1;
dshapes(2,0) = -1;
dshapes(2,1) = -1;
}
else
{
AutoDiff<2,T> x(xi(0), 0);
AutoDiff<2,T> y(xi(1), 1);
AutoDiff<2,T> lam3 = 1-x-y;
AutoDiff<2,T> shapes[6];
shapes[0] = x * (2*x-1);
shapes[1] = y * (2*y-1);
shapes[2] = lam3 * (2*lam3-1);
shapes[3] = 4 * y * lam3;
shapes[4] = 4 * x * lam3;
shapes[5] = 4 * x * y;
for (int i = 0; i < 6; i++)
{
dshapes(i,0) = shapes[i].DValue(0);
dshapes(i,1) = shapes[i].DValue(1);
}
}
break;
}
case QUAD:
{
dshapes(0,0) = -(1-xi(1));
dshapes(0,1) = -(1-xi(0));
dshapes(1,0) = (1-xi(1));
dshapes(1,1) = -xi(0);
dshapes(2,0) = xi(1);
dshapes(2,1) = xi(0);
dshapes(3,0) = -xi(1);
dshapes(3,1) = (1-xi(0));
if (info.order == 1) return;
T shapes[4] = {
(1-xi(0))*(1-xi(1)),
xi(0) *(1-xi(1)),
xi(0) * xi(1) ,
(1-xi(0))* xi(1)
};
T mu[4] = {
1 - xi(0) + 1 - xi(1),
xi(0) + 1 - xi(1),
xi(0) + xi(1),
1 - xi(0) + xi(1),
};
T dmu[4][2] = {
{ -1, -1 },
{ 1, -1 },
{ 1, 1 },
{ -1, 1 } };
// double hshapes[20], hdshapes[20];
NgArrayMem<T, 20> hshapes(order+1), hdshapes(order+1);
int ii = 4;
const ELEMENT_EDGE * edges = MeshTopology::GetEdges1 (QUAD);
for (int i = 0; i < 4; i++)
{
int eorder = edgeorder[info.edgenrs[i]];
if (eorder >= 2)
{
int vi1 = edges[i][0]-1, vi2 = edges[i][1]-1;
if (el[vi1] > el[vi2]) swap (vi1, vi2);
CalcEdgeShapeDx (eorder, mu[vi1]-mu[vi2], &hshapes[0], &hdshapes[0]);
T lame = shapes[vi1]+shapes[vi2];
T dlame[2] = {
dshapes(vi1, 0) + dshapes(vi2, 0),
dshapes(vi1, 1) + dshapes(vi2, 1) };
for (int j = 0; j < eorder-1; j++)
for (int k = 0; k < 2; k++)
dshapes(ii+j, k) =
lame * hdshapes[j] * (dmu[vi1][k]-dmu[vi2][k])
+ dlame[k] * hshapes[j];
ii += eorder-1;
}
}
/*
*testout << "quad, dshape = " << endl << dshapes << endl;
for (int i = 0; i < 2; i++)
{
Point<2> xil = xi, xir = xi;
Vector shapesl(dshapes.Height()), shapesr(dshapes.Height());
xil(i) -= 1e-6;
xir(i) += 1e-6;
CalcElementShapes (info, xil, shapesl);
CalcElementShapes (info, xir, shapesr);
for (int j = 0; j < dshapes.Height(); j++)
dshapes(j,i) = 1.0 / 2e-6 * (shapesr(j)-shapesl(j));
}
*testout << "quad, num dshape = " << endl << dshapes << endl;
*/
break;
}
default:
throw NgException("CurvedElements::CalcDShape 2d, element type not handled");
};
}
template <int DIM_SPACE, typename T>
bool CurvedElements ::
EvaluateMapping (SurfaceElementInfo & info, const Point<2,T> xi, Point<DIM_SPACE,T> & mx, Mat<DIM_SPACE,2,T> & jac) const
{
const Element2d & el = mesh[info.elnr];
if (rational && info.order >= 2) return false; // not supported
AutoDiff<2,T> x(xi(0), 0);
AutoDiff<2,T> y(xi(1), 1);
AutoDiff<2,T> mapped_x[DIM_SPACE];
for (int i = 0; i < DIM_SPACE; i++)
mapped_x[i] = AutoDiff<2,T>(0.0);
switch (el.GetType())
{
case TRIG6:
{
AutoDiff<2,T> lam3 = 1-x-y;
AutoDiff<2,T> lami[6] = { x * (2*x-1), y * (2*y-1), lam3 * (2*lam3-1),
4 * y * lam3, 4 * x * lam3, 4 * x * y };
for (int j = 0; j < 6; j++)
{
Point<3> p = mesh[el[j]];
for (int k = 0; k < DIM_SPACE; k++)
mapped_x[k] += p(k) * lami[j];
}
break;
}
case TRIG:
{
// if (info.order >= 2) return false; // not yet supported
AutoDiff<2,T> lami[4] = { x, y, 1-x-y };
for (int j = 0; j < 3; j++)
{
Point<3> p = mesh[el[j]];
for (int k = 0; k < DIM_SPACE; k++)
mapped_x[k] += p(k) * lami[j];
}
if (info.order == 1) break;
const ELEMENT_EDGE * edges = MeshTopology::GetEdges1 (TRIG);
for (int i = 0; i < 3; i++)
{
int eorder = edgeorder[info.edgenrs[i]];
if (eorder >= 2)
{
int first = edgecoeffsindex[info.edgenrs[i]];
int vi1 = edges[i][0]-1, vi2 = edges[i][1]-1;
if (el[vi1] > el[vi2]) swap (vi1, vi2);
CalcScaledEdgeShapeLambda (eorder, lami[vi1]-lami[vi2], lami[vi1]+lami[vi2],
[&](int i, AutoDiff<2,T> shape)
{
for (int k = 0; k < DIM_SPACE; k++)
mapped_x[k] += edgecoeffs[first+i](k) * shape;
});
}
}
int forder = faceorder[info.facenr];
if (forder >= 3)
{
int first = facecoeffsindex[info.facenr];
int fnums[] = { 0, 1, 2 };
if (el[fnums[0]] > el[fnums[1]]) swap (fnums[0], fnums[1]);
if (el[fnums[1]] > el[fnums[2]]) swap (fnums[1], fnums[2]);
if (el[fnums[0]] > el[fnums[1]]) swap (fnums[0], fnums[1]);
CalcScaledTrigShapeLambda (forder,
lami[fnums[1]]-lami[fnums[0]], lami[fnums[2]], AutoDiff<2,T>(1.0),
[&](int i, AutoDiff<2,T> shape)
{
for (int k = 0; k < DIM_SPACE; k++)
mapped_x[k] += facecoeffs[first+i](k) * shape;
});
}
break;
}
case QUAD:
{
if (info.order >= 2) return false; // not yet supported
AutoDiff<2,T> lami[4] = { (1-x)*(1-y), x*(1-y), x*y, (1-x)*y };
for (int j = 0; j < 4; j++)
{
Point<3> p = mesh[el[j]];
for (int k = 0; k < DIM_SPACE; k++)
mapped_x[k] += p(k) * lami[j];
}
break;
}
case QUAD8:
{
// AutoDiff<2,T> lami[4] = { (1-x)*(1-y), x*(1-y), x*y, (1-x)*y };
AutoDiff<2,T> lami[8] =
{ (1-x)*(1-y),
x*(1-y),
x*y,
(1-x)*y,
4*(1-x)*x*(1-y),
4*(1-x)*x*y,
4*(1-y)*y*(1-x),
4*(1-y)*y*x };
lami[0] -= 0.5*(lami[4]+lami[6]);
lami[1] -= 0.5*(lami[4]+lami[7]);
lami[2] -= 0.5*(lami[5]+lami[7]);
lami[3] -= 0.5*(lami[5]+lami[6]);
for (int j = 0; j < 8; j++)
{
Point<3> p = mesh[el[j]];
for (int k = 0; k < DIM_SPACE; k++)
mapped_x[k] += p(k) * lami[j];
}
break;
}
default:
return false;
}
for (int i = 0; i < DIM_SPACE; i++)
{
mx(i) = mapped_x[i].Value();
for (int j = 0; j < 2; j++)
jac(i,j) = mapped_x[i].DValue(j);
}
return true;
}
template <int DIM_SPACE>
void CurvedElements ::
GetCoefficients (SurfaceElementInfo & info, NgArray<Vec<DIM_SPACE> > & coefs) const
{
const Element2d & el = mesh[info.elnr];
coefs.SetSize (info.ndof);
for (int i = 0; i < info.nv; i++)
{
Point<3> hv = mesh[el[i]];
for (int j = 0; j < DIM_SPACE; j++)
coefs[i](j) = hv(j);
}
if (info.order == 1) return;
int ii = info.nv;
for (int i = 0; i < info.edgenrs.Size(); i++)
{
int first = edgecoeffsindex[info.edgenrs[i]];
int next = edgecoeffsindex[info.edgenrs[i]+1];
for (int j = first; j < next; j++, ii++)
for (int k = 0; k < DIM_SPACE; k++)
coefs[ii](k) = edgecoeffs[j](k);
}
int first = facecoeffsindex[info.facenr];
int next = facecoeffsindex[info.facenr+1];
for (int j = first; j < next; j++, ii++)
for (int k = 0; k < DIM_SPACE; k++)
coefs[ii](k) = facecoeffs[j](k);
}
template void CurvedElements ::
GetCoefficients<2> (SurfaceElementInfo & info, NgArray<Vec<2> > & coefs) const;
template void CurvedElements ::
GetCoefficients<3> (SurfaceElementInfo & info, NgArray<Vec<3> > & coefs) const;
// ********************** Transform volume elements *******************
bool CurvedElements :: IsElementCurved (ElementIndex elnr) const
{
if (mesh[elnr].GetType() != TET) return true;
if (mesh.coarsemesh)
{
const HPRefElement & hpref_el =
(*mesh.hpelements) [mesh[elnr].hp_elnr];
return mesh.coarsemesh->GetCurvedElements().IsElementCurved (hpref_el.coarse_elnr);
}
const Element & el = mesh[elnr];
ELEMENT_TYPE type = el.GetType();
int nfaces = MeshTopology::GetNFaces (type);
if (nfaces > 4)
{ // not a tet
const ELEMENT_FACE * faces = MeshTopology::GetFaces0 (type);
for (int j = 0; j < nfaces; j++)
{
if (faces[j][3] != -1)
{ // a quad face
Point<3> pts[4];
for (int k = 0; k < 4; k++)
pts[k] = mesh.Point(el[faces[j][k]]);
Vec<3> twist = (pts[1] - pts[0]) - (pts[2]-pts[3]);
if (twist.Length() > 1e-8 * (pts[1]-pts[0]).Length())
return true;
}
}
}
ElementInfo info;
info.elnr = elnr;
info.order = order;
info.ndof = info.nv = MeshTopology::GetNPoints (type);
if (info.order > 1)
{
const MeshTopology & top = mesh.GetTopology();
info.nedges = top.GetElementEdges (elnr+1, info.edgenrs, 0);
for (int i = 0; i < info.nedges; i++)
info.edgenrs[i]--;
info.nfaces = top.GetElementFaces (elnr+1, info.facenrs, 0);
for (int i = 0; i < info.nfaces; i++)
info.facenrs[i]--;
for (int i = 0; i < info.nedges; i++)
info.ndof += edgecoeffsindex[info.edgenrs[i]+1] - edgecoeffsindex[info.edgenrs[i]];
for (int i = 0; i < info.nfaces; i++)
info.ndof += facecoeffsindex[info.facenrs[i]+1] - facecoeffsindex[info.facenrs[i]];
}
return (info.ndof > info.nv);
}
bool CurvedElements :: IsElementHighOrder (ElementIndex elnr) const
{
if (mesh.coarsemesh)
{
const HPRefElement & hpref_el =
(*mesh.hpelements) [mesh[elnr].hp_elnr];
return mesh.coarsemesh->GetCurvedElements().IsElementHighOrder (hpref_el.coarse_elnr);
}
const Element & el = mesh[elnr];
ELEMENT_TYPE type = el.GetType();
ElementInfo info;
info.elnr = elnr;
info.order = order;
info.ndof = info.nv = MeshTopology::GetNPoints (type);
if (info.order > 1)
{
const MeshTopology & top = mesh.GetTopology();
info.nedges = top.GetElementEdges (elnr+1, info.edgenrs, 0);
for (int i = 0; i < info.nedges; i++) info.edgenrs[i]--;
info.nfaces = top.GetElementFaces (elnr+1, info.facenrs, 0);
for (int i = 0; i < info.nfaces; i++) info.facenrs[i]--;
for (int i = 0; i < info.nedges; i++)
if (edgecoeffsindex[info.edgenrs[i]+1] > edgecoeffsindex[info.edgenrs[i]]) return true;
for (int i = 0; i < info.nfaces; i++)
if (facecoeffsindex[info.facenrs[i]+1] > facecoeffsindex[info.facenrs[i]]) return true;
}
return false;
}
void CurvedElements ::
CalcElementTransformation (Point<3> xi, ElementIndex elnr,
Point<3> * x, Mat<3,3> * dxdxi, // bool * curved,
void * buffer, bool valid)
{
if (mesh.coarsemesh)
{
const HPRefElement & hpref_el =
(*mesh.hpelements) [mesh[elnr].hp_elnr];
// xi umrechnen
double lami[8];
FlatVector vlami(8, lami);
vlami = 0;
mesh[elnr].GetShapeNew<double> (xi, vlami);
Mat<3,3> trans, dxdxic;
if (dxdxi)
{
MatrixFixWidth<3> dlami(8);
dlami = 0;
mesh[elnr].GetDShapeNew (xi, dlami);
trans = 0;
for (int k = 0; k < 3; k++)
for (int l = 0; l < 3; l++)
for (int i = 0; i < hpref_el.np; i++)
trans(l,k) += hpref_el.param[i][l] * dlami(i, k);
}
Point<3> coarse_xi(0,0,0);
for (int i = 0; i < hpref_el.np; i++)
for (int j = 0; j < 3; j++)
coarse_xi(j) += hpref_el.param[i][j] * lami[i];
mesh.coarsemesh->GetCurvedElements().CalcElementTransformation (coarse_xi, hpref_el.coarse_elnr, x, &dxdxic /* , curved */);
if (dxdxi)
*dxdxi = dxdxic * trans;
return;
}
const Element & el = mesh[elnr];
ELEMENT_TYPE type = el.GetType();
ElementInfo hinfo;
ElementInfo & info = (buffer) ? *static_cast<ElementInfo*> (buffer) : hinfo;
if (!valid)
{
info.elnr = elnr;
info.order = order;
info.ndof = info.nv = MeshTopology::GetNPoints (type);
if (info.order > 1)
{
const MeshTopology & top = mesh.GetTopology();
info.nedges = top.GetElementEdges (elnr+1, info.edgenrs, 0);
for (int i = 0; i < info.nedges; i++)
info.edgenrs[i]--;
info.nfaces = top.GetElementFaces (elnr+1, info.facenrs, 0);
for (int i = 0; i < info.nfaces; i++)
info.facenrs[i]--;
for (int i = 0; i < info.nedges; i++)
info.ndof += edgecoeffsindex[info.edgenrs[i]+1] - edgecoeffsindex[info.edgenrs[i]];
for (int i = 0; i < info.nfaces; i++)
info.ndof += facecoeffsindex[info.facenrs[i]+1] - facecoeffsindex[info.facenrs[i]];
}
}
NgArrayMem<double,100> mem(info.ndof);
TFlatVector<double> shapes(info.ndof, &mem[0]);
NgArrayMem<double,100> dshapes_mem(info.ndof*3);
MatrixFixWidth<3> dshapes(info.ndof, &dshapes_mem[0]);
CalcElementShapes (info, xi, shapes);
Vec<3> * coefs = (info.ndof <= 10) ?
&info.hcoefs[0] : new Vec<3> [info.ndof];
if (info.ndof > 10 || !valid)
GetCoefficients (info, coefs);
if (x)
{
*x = 0;
for (int i = 0; i < shapes.Size(); i++)
*x += shapes(i) * coefs[i];
}
if (dxdxi)
{
if (valid && info.order == 1 && info.nv == 4) // a linear tet
{
*dxdxi = info.hdxdxi;
}
else
{
CalcElementDShapes (info, xi, dshapes);
*dxdxi = 0;
for (int i = 0; i < shapes.Size(); i++)
for (int j = 0; j < 3; j++)
for (int k = 0; k < 3; k++)
(*dxdxi)(j,k) += dshapes(i,k) * coefs[i](j);
info.hdxdxi = *dxdxi;
}
}
// *testout << "curved_elements, dshapes = " << endl << dshapes << endl;
// if (curved) *curved = (info.ndof > info.nv);
if (info.ndof > 10) delete [] coefs;
}
template <typename T>
void CurvedElements :: CalcElementShapes (ElementInfo & info, Point<3,T> xi, TFlatVector<T> shapes) const
{
const Element & el = mesh[info.elnr];
if (rational && info.order >= 2)
{
// shapes.SetSize(10);
T w = 1;
T lami[4] = { xi(0), xi(1), xi(2), 1-xi(0)-xi(1)-xi(2) };
for (int j = 0; j < 4; j++)
shapes(j) = lami[j] * lami[j];
const ELEMENT_EDGE * edges = MeshTopology::GetEdges1 (TET);
for (int j = 0; j < 6; j++)
{
double wi = edgeweight[info.edgenrs[j]];
shapes(j+4) = 2 * wi * lami[edges[j][0]-1] * lami[edges[j][1]-1];
w += (wi-1) * 2 * lami[edges[j][0]-1] * lami[edges[j][1]-1];
}
shapes *= 1.0 / w;
return;
}
// shapes.SetSize(info.ndof);
switch (el.GetType())
{
case TET:
{
shapes(0) = xi(0);
shapes(1) = xi(1);
shapes(2) = xi(2);
shapes(3) = 1-xi(0)-xi(1)-xi(2);
if (info.order == 1) return;
int ii = 4;
const ELEMENT_EDGE * edges = MeshTopology::GetEdges1 (TET);
for (int i = 0; i < 6; i++)
{
int eorder = edgeorder[info.edgenrs[i]];
if (eorder >= 2)
{
int vi1 = edges[i][0]-1, vi2 = edges[i][1]-1;
if (el[vi1] > el[vi2]) swap (vi1, vi2);
CalcScaledEdgeShape (eorder, shapes(vi1)-shapes(vi2), shapes(vi1)+shapes(vi2), &shapes(ii));
ii += eorder-1;
}
}
const ELEMENT_FACE * faces = MeshTopology::GetFaces1 (TET);
for (int i = 0; i < 4; i++)
{
int forder = faceorder[info.facenrs[i]];
if (forder >= 3)
{
int fnums[] = { faces[i][0]-1, faces[i][1]-1, faces[i][2]-1 };
if (el[fnums[0]] > el[fnums[1]]) swap (fnums[0], fnums[1]);
if (el[fnums[1]] > el[fnums[2]]) swap (fnums[1], fnums[2]);
if (el[fnums[0]] > el[fnums[1]]) swap (fnums[0], fnums[1]);
CalcScaledTrigShape (forder,
shapes(fnums[1])-shapes(fnums[0]), shapes(fnums[2]),
shapes(fnums[0])+shapes(fnums[1])+shapes(fnums[2]), &shapes(ii));
ii += (forder-1)*(forder-2)/2;
}
}
break;
}
case TET10:
{
T x = xi(0);
T y = xi(1);
T z = xi(2);
T lam4 = 1 - x - y - z;
/*
shapes(0) = xi(0);
shapes(1) = xi(1);
shapes(2) = xi(2);
shapes(3) = 1-xi(0)-xi(1)-xi(2);
*/
shapes(0) = 2 * x * x - x;
shapes(1) = 2 * y * y - y;
shapes(2) = 2 * z * z - z;
shapes(3) = 2 * lam4 * lam4 - lam4;
shapes(4) = 4 * x * y;
shapes(5) = 4 * x * z;
shapes(6) = 4 * x * lam4;
shapes(7) = 4 * y * z;
shapes(8) = 4 * y * lam4;
shapes(9) = 4 * z * lam4;
break;
}
case PRISM:
{
T lami[6] = { xi(0), xi(1), 1-xi(0)-xi(1), xi(0), xi(1), 1-xi(0)-xi(1) };
T lamiz[6] = { 1-xi(2), 1-xi(2), 1-xi(2), xi(2), xi(2), xi(2) };
for (int i = 0; i < 6; i++)
shapes(i) = lami[i] * lamiz[i];
for (int i = 6; i < info.ndof; i++)
shapes(i) = 0;
if (info.order == 1) return;
int ii = 6;
const ELEMENT_EDGE * edges = MeshTopology::GetEdges1 (PRISM);
for (int i = 0; i < 6; i++) // horizontal edges
{
int eorder = edgeorder[info.edgenrs[i]];
if (eorder >= 2)
{
int vi1 = edges[i][0]-1, vi2 = edges[i][1]-1;
if (el[vi1] > el[vi2]) swap (vi1, vi2);
CalcScaledEdgeShape (eorder, lami[vi1]-lami[vi2], lami[vi1]+lami[vi2], &shapes(ii));
T facz = (i < 3) ? (1-xi(2)) : xi(2);
for (int j = 0; j < eorder-1; j++)
shapes(ii+j) *= facz;
ii += eorder-1;
}
}
for (int i = 6; i < 9; i++) // vertical edges
{
int eorder = edgeorder[info.edgenrs[i]];
if (eorder >= 2)
{
int vi1 = edges[i][0]-1, vi2 = edges[i][1]-1;
if (el[vi1] > el[vi2]) swap (vi1, vi2);
T bubz = lamiz[vi1]*lamiz[vi2];
T polyz = lamiz[vi1] - lamiz[vi2];
T bubxy = lami[vi1];
for (int j = 0; j < eorder-1; j++)
{
shapes(ii+j) = bubxy * bubz;
bubz *= polyz;
}
ii += eorder-1;
}
}
// FACE SHAPES
const ELEMENT_FACE * faces = MeshTopology::GetFaces1 (PRISM);
for (int i = 0; i < 2; i++)
{
int forder = faceorder[info.facenrs[i]];
if ( forder < 3 ) continue;
int fav[3] = { faces[i][0]-1, faces[i][1]-1, faces[i][2]-1 };
if(el[fav[0]] > el[fav[1]]) swap(fav[0],fav[1]);
if(el[fav[1]] > el[fav[2]]) swap(fav[1],fav[2]);
if(el[fav[0]] > el[fav[1]]) swap(fav[0],fav[1]);
CalcTrigShape (forder,
lami[fav[2]]-lami[fav[1]], lami[fav[0]],
&shapes(ii));
int ndf = (forder+1)*(forder+2)/2 - 3 - 3*(forder-1);
for ( int j = 0; j < ndf; j++ )
shapes(ii+j) *= lamiz[fav[1]];
ii += ndf;
}
break;
}
case PRISM15:
{
shapes = 0.0;
T x = xi(0);
T y = xi(1);
T z = xi(2);
T lam = 1-x-y;
T lamz = 1-z;
shapes[0] = (2*x*x-x) * (2*lamz*lamz-lamz);
shapes[1] = (2*y*y-y) * (2*lamz*lamz-lamz);
shapes[2] = (2*lam*lam-lam) * (2*lamz*lamz-lamz);
shapes[3] = (2*x*x-x) * (2*z*z-z);
shapes[4] = (2*y*y-y) * (2*z*z-z);
shapes[5] = (2*lam*lam-lam) * (2*z*z-z);
shapes[6] = 4 * x * y * (2*lamz*lamz-lamz);
shapes[7] = 4 * x * lam * (2*lamz*lamz-lamz);
shapes[8] = 4 * y * lam * (2*lamz*lamz-lamz);
shapes[9] = x * 4 * z * (1-z);
shapes[10] = y * 4 * z * (1-z);
shapes[11] = lam * 4 * z * (1-z);
shapes[12] = 4 * x * y * (2*z*z-z);
shapes[13] = 4 * x * lam * (2*z*z-z);
shapes[14] = 4 * y * lam * (2*z*z-z);
break;
}
case PYRAMID:
{
shapes = 0.0;
T x = xi(0);
T y = xi(1);
T z = xi(2);
// if (z == 1.) z = 1-1e-10;
z *= (1-1e-12);
shapes[0] = (1-z-x)*(1-z-y) / (1-z);
shapes[1] = x*(1-z-y) / (1-z);
shapes[2] = x*y / (1-z);
shapes[3] = (1-z-x)*y / (1-z);
shapes[4] = z;
if (info.order == 1) return;
T sigma[4] =
{
sigma[0] = ( (1-z-x) + (1-z-y) ),
sigma[1] = ( x + (1-z-y) ),
sigma[2] = ( x + y ),
sigma[3] = ( (1-z-x) + y ),
};
int ii = 5;
const ELEMENT_EDGE * edges = MeshTopology::GetEdges1 (PYRAMID);
for (int i = 0; i < 4; i++) // horizontal edges
{
int eorder = edgeorder[info.edgenrs[i]];
if (eorder >= 2)
{
int vi1 = (edges[i][0]-1), vi2 = (edges[i][1]-1);
if (el[vi1] > el[vi2]) swap (vi1, vi2);
CalcScaledEdgeShape (eorder, sigma[vi1]-sigma[vi2], 1-z, &shapes(ii));
T fac = (shapes[vi1]+shapes[vi2]) / (1-z);
for (int j = 0; j < eorder-1; j++)
shapes(ii+j) *= fac;
ii += eorder-1;
}
}
break;
}
case PYRAMID13:
{
shapes = 0.0;
T x = xi(0);
T y = xi(1);
T z = xi(2);
z *= 1-1e-12;
shapes[0] = (-z + z*(2*x + z - 1)*(2*y + z - 1)/(-z + 1) + (-2*x - z + 2)*(-2*y - z + 2))*(-0.5*x - 0.5*y - 0.5*z + 0.25);
shapes[1] = (0.5*x - 0.5*y - 0.25)*(-z - z*(2*x + z - 1)*(2*y + z - 1)/(-z + 1) + (2*x + z)*(-2*y - z + 2));
shapes[2] = (-z + z*(2*x + z - 1)*(2*y + z - 1)/(-z + 1) + (2*x + z)*(2*y + z))*(0.5*x + 0.5*y + 0.5*z - 0.75);
shapes[3] = (-0.5*x + 0.5*y - 0.25)*(-z - z*(2*x + z - 1)*(2*y + z - 1)/(-z + 1) + (2*y + z)*(-2*x - z + 2));
shapes[4] = z*(2*z - 1);
shapes[5] = 2*x*(-2*x - 2*z + 2)*(-2*y - 2*z + 2)/(-2*z + 2);
shapes[6] = 4*x*y*(-2*x - 2*z + 2)/(-2*z + 2);
shapes[7] = 2*y*(-2*x - 2*z + 2)*(-2*y - 2*z + 2)/(-2*z + 2);
shapes[8] = 4*x*y*(-2*y - 2*z + 2)/(-2*z + 2);
shapes[9] = z*(-2*x - 2*z + 2)*(-2*y - 2*z + 2)/(-z + 1);
shapes[10] = 2*x*z*(-2*y - 2*z + 2)/(-z + 1);
shapes[11] = 4*x*y*z/(-z + 1);
shapes[12] = 2*y*z*(-2*x - 2*z + 2)/(-z + 1);
break;
}
case HEX:
{
shapes = 0.0;
T x = xi(0);
T y = xi(1);
T z = xi(2);
shapes[0] = (1-x)*(1-y)*(1-z);
shapes[1] = x *(1-y)*(1-z);
shapes[2] = x * y *(1-z);
shapes[3] = (1-x)* y *(1-z);
shapes[4] = (1-x)*(1-y)*(z);
shapes[5] = x *(1-y)*(z);
shapes[6] = x * y *(z);
shapes[7] = (1-x)* y *(z);
if (info.order == 1) return;
T mu[8] = {
(1-x)+(1-y)+(1-z),
x +(1-y)+(1-z),
x + y +(1-z),
(1-x)+ y +(1-z),
(1-x)+(1-y)+(z),
x +(1-y)+(z),
x + y +(z),
(1-x)+ y +(z),
};
int ii = 8;
const ELEMENT_EDGE * edges = MeshTopology::GetEdges1 (HEX);
for (int i = 0; i < 12; i++)
{
int eorder = edgeorder[info.edgenrs[i]];
if (eorder >= 2)
{
int vi1 = edges[i][0]-1, vi2 = edges[i][1]-1;
if (el[vi1] > el[vi2]) swap (vi1, vi2);
CalcEdgeShape (eorder, mu[vi1]-mu[vi2], &shapes(ii));
T lame = shapes(vi1)+shapes(vi2);
for (int j = 0; j < order-1; j++)
shapes(ii+j) *= lame;
ii += eorder-1;
}
}
break;
}
case HEX20:
{
shapes = 0.0;
T x = xi(0);
T y = xi(1);
T z = xi(2);
shapes[0] = (1-x)*(1-y)*(1-z);
shapes[1] = x *(1-y)*(1-z);
shapes[2] = x * y *(1-z);
shapes[3] = (1-x)* y *(1-z);
shapes[4] = (1-x)*(1-y)*(z);
shapes[5] = x *(1-y)*(z);
shapes[6] = x * y *(z);
shapes[7] = (1-x)* y *(z);
T sigma[8]={(1-x)+(1-y)+(1-z),x+(1-y)+(1-z),x+y+(1-z),(1-x)+y+(1-z),
(1-x)+(1-y)+z,x+(1-y)+z,x+y+z,(1-x)+y+z};
static const int e[12][2] =
{
{ 0, 1 }, { 2, 3 }, { 3, 0 }, { 1, 2 },
{ 4, 5 }, { 6, 7 }, { 7, 4 }, { 5, 6 },
{ 0, 4 }, { 1, 5 }, { 2, 6 }, { 3, 7 },
};
for (int i = 0; i < 12; i++)
{
T lame = shapes[e[i][0]]+shapes[e[i][1]];
T xi = sigma[e[i][1]]-sigma[e[i][0]];
shapes[8+i] = (1-xi*xi)*lame;
}
for (int i = 0; i < 12; i++)
{
shapes[e[i][0]] -= 0.5 * shapes[8+i];
shapes[e[i][1]] -= 0.5 * shapes[8+i];
}
break;
}
default:
throw NgException("CurvedElements::CalcShape 3d, element type not handled");
};
}
template <typename T>
void CurvedElements ::
CalcElementDShapes (ElementInfo & info, const Point<3,T> xi, MatrixFixWidth<3,T> & dshapes) const
{
// static int timer = NgProfiler::CreateTimer ("calcelementdshapes");
const Element & el = mesh[info.elnr];
// dshapes.SetSize(info.ndof);
if ( (long int)(&dshapes(0,0)) % alignof(T) != 0)
throw NgException ("alignment problem");
if (dshapes.Height() != info.ndof)
throw NgException ("wrong height");
if (rational && info.order >= 2)
{
T w = 1;
T dw[3] = { 0, 0, 0 };
T lami[4] = { xi(0), xi(1), xi(2), 1-xi(0)-xi(1)-xi(2) };
T dlami[4][3] = { { 1, 0, 0 }, { 0, 1, 0 }, { 0, 0, 1 }, { -1, -1, -1 }};
T shapes[10];
for (int j = 0; j < 4; j++)
{
shapes[j] = lami[j] * lami[j];
dshapes(j,0) = 2 * lami[j] * dlami[j][0];
dshapes(j,1) = 2 * lami[j] * dlami[j][1];
dshapes(j,2) = 2 * lami[j] * dlami[j][2];
}
const ELEMENT_EDGE * edges = MeshTopology::GetEdges1 (TET);
for (int j = 0; j < 6; j++)
{
T wi = edgeweight[info.edgenrs[j]];
shapes[j+4] = 2 * wi * lami[edges[j][0]-1] * lami[edges[j][1]-1];
for (int k = 0; k < 3; k++)
dshapes(j+4,k) = 2*wi* (lami[edges[j][0]-1] * dlami[edges[j][1]-1][k] +
lami[edges[j][1]-1] * dlami[edges[j][0]-1][k]);
w += (wi-1) * 2 * lami[edges[j][0]-1] * lami[edges[j][1]-1];
for (int k = 0; k < 3; k++)
dw[k] += 2*(wi-1) * (lami[edges[j][0]-1] * dlami[edges[j][1]-1][k] +
lami[edges[j][1]-1] * dlami[edges[j][0]-1][k]);
}
// shapes *= 1.0 / w;
dshapes *= 1.0 / w;
for (int i = 0; i < 10; i++)
for (int j = 0; j < 3; j++)
dshapes(i,j) -= shapes[i] * dw[j] / (w*w);
return;
}
/*
if (typeid(T) == typeid(SIMD<double>))
{
if (el.GetType() == HEX)
dshapes = T(0.0);
return;
}
*/
switch (el.GetType())
{
case TET:
{
// if (typeid(T) == typeid(SIMD<double>)) return;
dshapes = T(0.0);
dshapes(0,0) = 1;
dshapes(1,1) = 1;
dshapes(2,2) = 1;
dshapes(3,0) = -1;
dshapes(3,1) = -1;
dshapes(3,2) = -1;
if (info.order == 1) return;
T lami[] = { xi(0), xi(1), xi(2), 1-xi(0)-xi(1)-xi(2) };
int ii = 4;
const ELEMENT_EDGE * edges = MeshTopology::GetEdges1 (TET);
for (int i = 0; i < 6; i++)
{
int eorder = edgeorder[info.edgenrs[i]];
if (eorder >= 2)
{
int vi1 = edges[i][0]-1, vi2 = edges[i][1]-1;
if (el[vi1] > el[vi2]) swap (vi1, vi2);
CalcScaledEdgeShapeDxDt<3> (eorder, lami[vi1]-lami[vi2], lami[vi1]+lami[vi2], &dshapes(ii,0));
Mat<2,3,T> trans;
for (int j = 0; j < 3; j++)
{
trans(0,j) = dshapes(vi1,j)-dshapes(vi2,j);
trans(1,j) = dshapes(vi1,j)+dshapes(vi2,j);
}
for (int j = 0; j < order-1; j++)
{
T ddx = dshapes(ii+j,0);
T ddt = dshapes(ii+j,1);
dshapes(ii+j,0) = ddx * trans(0,0) + ddt * trans(1,0);
dshapes(ii+j,1) = ddx * trans(0,1) + ddt * trans(1,1);
dshapes(ii+j,2) = ddx * trans(0,2) + ddt * trans(1,2);
}
ii += eorder-1;
}
}
const ELEMENT_FACE * faces = MeshTopology::GetFaces1 (TET);
for (int i = 0; i < 4; i++)
{
int forder = faceorder[info.facenrs[i]];
if (forder >= 3)
{
int fnums[] = { faces[i][0]-1, faces[i][1]-1, faces[i][2]-1 };
if (el[fnums[0]] > el[fnums[1]]) swap (fnums[0], fnums[1]);
if (el[fnums[1]] > el[fnums[2]]) swap (fnums[1], fnums[2]);
if (el[fnums[0]] > el[fnums[1]]) swap (fnums[0], fnums[1]);
CalcScaledTrigShapeDxDyDt (forder,
lami[fnums[1]]-lami[fnums[0]],
lami[fnums[2]], lami[fnums[0]]+lami[fnums[1]]+lami[fnums[2]],
&dshapes(ii,0));
Mat<3,3,T> trans;
for (int j = 0; j < 3; j++)
{
trans(0,j) = dshapes(fnums[1],j)-dshapes(fnums[0],j);
trans(1,j) = dshapes(fnums[2],j);
trans(2,j) = dshapes(fnums[0],j)+dshapes(fnums[1],j)+dshapes(fnums[2],j);
}
int nfd = (forder-1)*(forder-2)/2;
for (int j = 0; j < nfd; j++)
{
T ddx = dshapes(ii+j,0);
T ddy = dshapes(ii+j,1);
T ddt = dshapes(ii+j,2);
dshapes(ii+j,0) = ddx * trans(0,0) + ddy * trans(1,0) + ddt * trans(2,0);
dshapes(ii+j,1) = ddx * trans(0,1) + ddy * trans(1,1) + ddt * trans(2,1);
dshapes(ii+j,2) = ddx * trans(0,2) + ddy * trans(1,2) + ddt * trans(2,2);
}
ii += nfd;
}
}
break;
}
case TET10:
{
// if (typeid(T) == typeid(SIMD<double>)) return;
if (dshapes.Height() == 4)
{
dshapes = T(0.0);
dshapes(0,0) = 1;
dshapes(1,1) = 1;
dshapes(2,2) = 1;
dshapes(3,0) = -1;
dshapes(3,1) = -1;
dshapes(3,2) = -1;
}
else
{
AutoDiff<3,T> x(xi(0), 0);
AutoDiff<3,T> y(xi(1), 1);
AutoDiff<3,T> z(xi(2), 2);
AutoDiff<3,T> lam4 = 1-x-y-z;
AutoDiff<3,T> shapes[10];
shapes[0] = 2 * x * x - x;
shapes[1] = 2 * y * y - y;
shapes[2] = 2 * z * z - z;
shapes[3] = 2 * lam4 * lam4 - lam4;
shapes[4] = 4 * x * y;
shapes[5] = 4 * x * z;
shapes[6] = 4 * x * lam4;
shapes[7] = 4 * y * z;
shapes[8] = 4 * y * lam4;
shapes[9] = 4 * z * lam4;
for (int i = 0; i < 10; i++)
{
dshapes(i,0) = shapes[i].DValue(0);
dshapes(i,1) = shapes[i].DValue(1);
dshapes(i,2) = shapes[i].DValue(2);
}
}
break;
break;
}
case PRISM:
{
T lami[6] = { xi(0), xi(1), 1-xi(0)-xi(1), xi(0), xi(1), 1-xi(0)-xi(1) };
T lamiz[6] = { 1-xi(2), 1-xi(2), 1-xi(2), xi(2), xi(2), xi(2) };
T dlamiz[6] = { -1, -1, -1, 1, 1, 1 };
T dlami[6][2] =
{ { 1, 0, },
{ 0, 1, },
{ -1, -1 },
{ 1, 0, },
{ 0, 1, },
{ -1, -1 } };
for (int i = 0; i < 6; i++)
{
// shapes(i) = lami[i%3] * ( (i < 3) ? (1-xi(2)) : xi(2) );
dshapes(i,0) = dlami[i%3][0] * ( (i < 3) ? (1-xi(2)) : xi(2) );
dshapes(i,1) = dlami[i%3][1] * ( (i < 3) ? (1-xi(2)) : xi(2) );
dshapes(i,2) = lami[i%3] * ( (i < 3) ? -1 : 1 );
}
int ii = 6;
if (info.order == 1) return;
const ELEMENT_EDGE * edges = MeshTopology::GetEdges1 (PRISM);
for (int i = 0; i < 6; i++) // horizontal edges
{
int order = edgeorder[info.edgenrs[i]];
if (order >= 2)
{
int vi1 = (edges[i][0]-1), vi2 = (edges[i][1]-1);
if (el[vi1] > el[vi2]) swap (vi1, vi2);
vi1 = vi1 % 3;
vi2 = vi2 % 3;
NgArrayMem<T,20> shapei_mem(order+1);
TFlatVector<T> shapei(order+1, &shapei_mem[0]);
CalcScaledEdgeShapeDxDt<3> (order, lami[vi1]-lami[vi2], lami[vi1]+lami[vi2], &dshapes(ii,0) );
CalcScaledEdgeShape(order, lami[vi1]-lami[vi2], lami[vi1]+lami[vi2], &shapei(0) );
Mat<2,2,T> trans;
for (int j = 0; j < 2; j++)
{
trans(0,j) = dlami[vi1][j]-dlami[vi2][j];
trans(1,j) = dlami[vi1][j]+dlami[vi2][j];
}
for (int j = 0; j < order-1; j++)
{
T ddx = dshapes(ii+j,0);
T ddt = dshapes(ii+j,1);
dshapes(ii+j,0) = ddx * trans(0,0) + ddt * trans(1,0);
dshapes(ii+j,1) = ddx * trans(0,1) + ddt * trans(1,1);
}
T facz = (i < 3) ? (1-xi(2)) : xi(2);
T dfacz = (i < 3) ? (-1) : 1;
for (int j = 0; j < order-1; j++)
{
dshapes(ii+j,0) *= facz;
dshapes(ii+j,1) *= facz;
dshapes(ii+j,2) = shapei(j) * dfacz;
}
ii += order-1;
}
}
// if (typeid(T) == typeid(SIMD<double>)) return;
for (int i = 6; i < 9; i++) // vertical edges
{
int eorder = edgeorder[info.edgenrs[i]];
if (eorder >= 2)
{
int vi1 = (edges[i][0]-1), vi2 = (edges[i][1]-1);
if (el[vi1] > el[vi2]) swap (vi1, vi2);
T bubz = lamiz[vi1] * lamiz[vi2];
T dbubz = dlamiz[vi1]*lamiz[vi2] + lamiz[vi1]*dlamiz[vi2];
T polyz = lamiz[vi1] - lamiz[vi2];
T dpolyz = dlamiz[vi1] - dlamiz[vi2];
T bubxy = lami[(vi1)%3];
T dbubxydx = dlami[(vi1)%3][0];
T dbubxydy = dlami[(vi1)%3][1];
for (int j = 0; j < eorder-1; j++)
{
dshapes(ii+j,0) = dbubxydx * bubz;
dshapes(ii+j,1) = dbubxydy * bubz;
dshapes(ii+j,2) = bubxy * dbubz;
dbubz = bubz * dpolyz + dbubz * polyz;
bubz *= polyz;
}
ii += eorder-1;
}
}
if (info.order == 2) return;
// FACE SHAPES
const ELEMENT_FACE * faces = MeshTopology::GetFaces1 (PRISM);
for (int i = 0; i < 2; i++)
{
int forder = faceorder[info.facenrs[i]];
if ( forder < 3 ) continue;
int ndf = (forder+1)*(forder+2)/2 - 3 - 3*(forder-1);
int fav[3] = { faces[i][0]-1, faces[i][1]-1, faces[i][2]-1 };
if(el[fav[0]] > el[fav[1]]) swap(fav[0],fav[1]);
if(el[fav[1]] > el[fav[2]]) swap(fav[1],fav[2]);
if(el[fav[0]] > el[fav[1]]) swap(fav[0],fav[1]);
NgArrayMem<T,2*20> dshapei_mem(ndf);
NgArrayMem<T,20> shapei_mem(ndf);
MatrixFixWidth<2,T> dshapei(ndf, &dshapei_mem[0]);
TFlatVector<T> shapei(ndf, &shapei_mem[0]);
CalcTrigShapeDxDy (forder,
lami[fav[2]]-lami[fav[1]], lami[fav[0]],
&dshapei(0,0));
CalcTrigShape (forder, lami[fav[2]]-lami[fav[1]], lami[fav[0]],
&shapei(0));
Mat<2,2,T> trans;
for (int j = 0; j < 2; j++)
{
trans(0,j) = dlami[fav[2]][j]-dlami[fav[1]][j];
trans(1,j) = dlami[fav[0]][j];
}
for (int j = 0; j < ndf; j++)
{
// double ddx = dshapes(ii+j,0);
// double ddt = dshapes(ii+j,1);
T ddx = dshapei(j,0);
T ddt = dshapei(j,1);
dshapes(ii+j,0) = ddx * trans(0,0) + ddt * trans(1,0);
dshapes(ii+j,1) = ddx * trans(0,1) + ddt * trans(1,1);
}
for ( int j = 0; j < ndf; j++ )
{
dshapes(ii+j,0) *= lamiz[fav[1]];
dshapes(ii+j,1) *= lamiz[fav[1]];
dshapes(ii+j,2) = shapei(j) * dlamiz[fav[1]];
}
ii += ndf;
}
break;
}
case PRISM15:
{
AutoDiff<3,T> x(xi(0), 0);
AutoDiff<3,T> y(xi(1), 1);
AutoDiff<3,T> z(xi(2), 2);
AutoDiff<3,T> ad[15];
AutoDiff<3,T> lam = 1-x-y;
AutoDiff<3,T> lamz = 1-z;
ad[0] = (2*x*x-x) * (2*lamz*lamz-lamz);
ad[1] = (2*y*y-y) * (2*lamz*lamz-lamz);
ad[2] = (2*lam*lam-lam) * (2*lamz*lamz-lamz);
ad[3] = (2*x*x-x) * (2*z*z-z);
ad[4] = (2*y*y-y) * (2*z*z-z);
ad[5] = (2*lam*lam-lam) * (2*z*z-z);
ad[6] = 4 * x * y * (2*lamz*lamz-lamz);
ad[7] = 4 * x * lam * (2*lamz*lamz-lamz);
ad[8] = 4 * y * lam * (2*lamz*lamz-lamz);
ad[9] = x * 4 * z * (1-z);
ad[10] = y * 4 * z * (1-z);
ad[11] = lam * 4 * z * (1-z);
ad[12] = 4 * x * y * (2*z*z-z);
ad[13] = 4 * x * lam * (2*z*z-z);
ad[14] = 4 * y * lam * (2*z*z-z);
for(int i=0; i<15; i++)
for(int j=0; j<3; j++)
dshapes(i,j) = ad[i].DValue(j);
break;
}
case PYRAMID:
{
// if (typeid(T) == typeid(SIMD<double>)) return;
dshapes = T(0.0);
T x = xi(0);
T y = xi(1);
T z = xi(2);
// if (z == 1.) z = 1-1e-10;
z *= 1-1e-12;
T z1 = 1-z;
T z2 = z1*z1;
dshapes(0,0) = -(z1-y)/z1;
dshapes(0,1) = -(z1-x)/z1;
dshapes(0,2) = ((x+y+2*z-2)*z1+(z1-y)*(z1-x))/z2;
dshapes(1,0) = (z1-y)/z1;
dshapes(1,1) = -x/z1;
dshapes(1,2) = (-x*z1+x*(z1-y))/z2;
dshapes(2,0) = y/z1;
dshapes(2,1) = x/z1;
dshapes(2,2) = x*y/z2;
dshapes(3,0) = -y/z1;
dshapes(3,1) = (z1-x)/z1;
dshapes(3,2) = (-y*z1+y*(z1-x))/z2;
dshapes(4,0) = 0;
dshapes(4,1) = 0;
dshapes(4,2) = 1;
if (info.order == 1) return;
int ii = 5;
const ELEMENT_EDGE * edges = MeshTopology::GetEdges1 (PYRAMID);
// if (z == 1.) z = 1-1e-10;
z *= 1-1e-12;
T shapes[5];
shapes[0] = (1-z-x)*(1-z-y) / (1-z);
shapes[1] = x*(1-z-y) / (1-z);
shapes[2] = x*y / (1-z);
shapes[3] = (1-z-x)*y / (1-z);
shapes[4] = z;
T sigma[4] =
{
( (1-z-x) + (1-z-y) ),
( x + (1-z-y) ),
( x + y ),
( (1-z-x) + y ),
};
T dsigma[4][3] =
{
{ -1, -1, -2 },
{ 1, -1, -1 },
{ 1, 1, 0 },
{ -1, 1, -1 }
};
T dz[3] = { 0, 0, 1 };
for (int i = 0; i < 4; i++) // horizontal edges
{
int eorder = edgeorder[info.edgenrs[i]];
if (eorder >= 2)
{
int vi1 = (edges[i][0]-1), vi2 = (edges[i][1]-1);
if (el[vi1] > el[vi2]) swap (vi1, vi2);
NgArrayMem<T,20> shapei_mem(eorder+1);
TFlatVector<T> shapei(eorder+1,&shapei_mem[0]);
CalcScaledEdgeShapeDxDt<3> (eorder, sigma[vi1]-sigma[vi2], 1-z, &dshapes(ii,0) );
CalcScaledEdgeShape(eorder, sigma[vi1]-sigma[vi2], 1-z, &shapei(0) );
T fac = (shapes[vi1]+shapes[vi2]) / (1-z);
T dfac[3];
for (int k = 0; k < 3; k++)
dfac[k] = ( (dshapes(vi1,k)+dshapes(vi2,k)) * (1-z) -
(shapes[vi1]+shapes[vi2]) *(-dshapes(4,k)) )
/ sqr(1-z);
for (int j = 0; j < eorder-1; j++)
{
T ddx = dshapes(ii+j,0);
T ddt = dshapes(ii+j,1);
for (int k = 0; k < 3; k++)
dshapes(ii+j,k) = fac * (ddx * (dsigma[vi1][k]-dsigma[vi2][k]) - ddt*dz[k])
+ dfac[k] * shapei(j);
}
ii += eorder-1;
}
}
break;
}
case PYRAMID13:
{
T x = xi(0);
T y = xi(1);
T z = xi(2);
z *= 1-1e-12;
dshapes(0,0) = 0.5*z - 0.5*z*(2*x + z - 1)*(2*y + z - 1)/(-z + 1) - 0.5*(-2*x - z + 2)*(-2*y - z + 2) + (-0.5*x - 0.5*y - 0.5*z + 0.25)*(4*y + 2*z + 2*z*(2*y + z - 1)/(-z + 1) - 4);
dshapes(0,1) = 0.5*z - 0.5*z*(2*x + z - 1)*(2*y + z - 1)/(-z + 1) - 0.5*(-2*x - z + 2)*(-2*y - z + 2) + (-0.5*x - 0.5*y - 0.5*z + 0.25)*(4*x + 2*z + 2*z*(2*x + z - 1)/(-z + 1) - 4);
dshapes(0,2) = 0.5*z - 0.5*z*(2*x + z - 1)*(2*y + z - 1)/(-z + 1) - 0.5*(-2*x - z + 2)*(-2*y - z + 2) + (-0.5*x - 0.5*y - 0.5*z + 0.25)*(2*x + 2*y + 2*z + z*(2*x + z - 1)/(-z + 1) + z*(2*y + z - 1)/(-z + 1) + z*(2*x + z - 1)*(2*y + z - 1)/((-z + 1)*(-z + 1)) - 5 + (2*x + z - 1)*(2*y + z - 1)/(-z + 1));
dshapes(1,0) = -0.5*z - 0.5*z*(2*x + z - 1)*(2*y + z - 1)/(-z + 1) + 0.5*(2*x + z)*(-2*y - z + 2) + (0.5*x - 0.5*y - 0.25)*(-4*y - 2*z - 2*z*(2*y + z - 1)/(-z + 1) + 4);
dshapes(1,1) = 0.5*z + 0.5*z*(2*x + z - 1)*(2*y + z - 1)/(-z + 1) - 0.5*(2*x + z)*(-2*y - z + 2) + (-4*x - 2*z - 2*z*(2*x + z - 1)/(-z + 1))*(0.5*x - 0.5*y - 0.25);
dshapes(1,2) = (0.5*x - 0.5*y - 0.25)*(-2*x - 2*y - 2*z - z*(2*x + z - 1)/(-z + 1) - z*(2*y + z - 1)/(-z + 1) - z*(2*x + z - 1)*(2*y + z - 1)/((-z + 1)*(-z + 1)) + 1 - (2*x + z - 1)*(2*y + z - 1)/(-z + 1));
dshapes(2,0) = -0.5*z + 0.5*z*(2*x + z - 1)*(2*y + z - 1)/(-z + 1) + 0.5*(2*x + z)*(2*y + z) + (4*y + 2*z + 2*z*(2*y + z - 1)/(-z + 1))*(0.5*x + 0.5*y + 0.5*z - 0.75);
dshapes(2,1) = -0.5*z + 0.5*z*(2*x + z - 1)*(2*y + z - 1)/(-z + 1) + 0.5*(2*x + z)*(2*y + z) + (4*x + 2*z + 2*z*(2*x + z - 1)/(-z + 1))*(0.5*x + 0.5*y + 0.5*z - 0.75);
dshapes(2,2) = -0.5*z + 0.5*z*(2*x + z - 1)*(2*y + z - 1)/(-z + 1) + 0.5*(2*x + z)*(2*y + z) + (0.5*x + 0.5*y + 0.5*z - 0.75)*(2*x + 2*y + 2*z + z*(2*x + z - 1)/(-z + 1) + z*(2*y + z - 1)/(-z + 1) + z*(2*x + z - 1)*(2*y + z - 1)/((-z + 1)*(-z + 1)) - 1 + (2*x + z - 1)*(2*y + z - 1)/(-z + 1));
dshapes(3,0) = 0.5*z + 0.5*z*(2*x + z - 1)*(2*y + z - 1)/(-z + 1) - 0.5*(2*y + z)*(-2*x - z + 2) + (-0.5*x + 0.5*y - 0.25)*(-4*y - 2*z - 2*z*(2*y + z - 1)/(-z + 1));
dshapes(3,1) = -0.5*z - 0.5*z*(2*x + z - 1)*(2*y + z - 1)/(-z + 1) + 0.5*(2*y + z)*(-2*x - z + 2) + (-0.5*x + 0.5*y - 0.25)*(-4*x - 2*z - 2*z*(2*x + z - 1)/(-z + 1) + 4);
dshapes(3,2) = (-0.5*x + 0.5*y - 0.25)*(-2*x - 2*y - 2*z - z*(2*x + z - 1)/(-z + 1) - z*(2*y + z - 1)/(-z + 1) - z*(2*x + z - 1)*(2*y + z - 1)/((-z + 1)*(-z + 1)) + 1 - (2*x + z - 1)*(2*y + z - 1)/(-z + 1));
dshapes(4,0) = 0;
dshapes(4,1) = 0;
dshapes(4,2) = 4*z - 1;
dshapes(5,0) = -4*x*(-2*y - 2*z + 2)/(-2*z + 2) + 2*(-2*x - 2*z + 2)*(-2*y - 2*z + 2)/(-2*z + 2);
dshapes(5,1) = -4*x*(-2*x - 2*z + 2)/(-2*z + 2);
dshapes(5,2) = -4*x*(-2*x - 2*z + 2)/(-2*z + 2) - 4*x*(-2*y - 2*z + 2)/(-2*z + 2) + 4*x*(-2*x - 2*z + 2)*(-2*y - 2*z + 2)/((-2*z + 2)*(-2*z + 2));
dshapes(6,0) = -8*x*y/(-2*z + 2) + 4*y*(-2*x - 2*z + 2)/(-2*z + 2);
dshapes(6,1) = 4*x*(-2*x - 2*z + 2)/(-2*z + 2);
dshapes(6,2) = -8*x*y/(-2*z + 2) + 8*x*y*(-2*x - 2*z + 2)/((-2*z + 2)*(-2*z + 2));
dshapes(7,0) = -4*y*(-2*y - 2*z + 2)/(-2*z + 2);
dshapes(7,1) = -4*y*(-2*x - 2*z + 2)/(-2*z + 2) + 2*(-2*x - 2*z + 2)*(-2*y - 2*z + 2)/(-2*z + 2);
dshapes(7,2) = -4*y*(-2*x - 2*z + 2)/(-2*z + 2) - 4*y*(-2*y - 2*z + 2)/(-2*z + 2) + 4*y*(-2*x - 2*z + 2)*(-2*y - 2*z + 2)/((-2*z + 2)*(-2*z + 2));
dshapes(8,0) = 4*y*(-2*y - 2*z + 2)/(-2*z + 2);
dshapes(8,1) = -8*x*y/(-2*z + 2) + 4*x*(-2*y - 2*z + 2)/(-2*z + 2);
dshapes(8,2) = -8*x*y/(-2*z + 2) + 8*x*y*(-2*y - 2*z + 2)/((-2*z + 2)*(-2*z + 2));
dshapes(9,0) = -2*z*(-2*y - 2*z + 2)/(-z + 1);
dshapes(9,1) = -2*z*(-2*x - 2*z + 2)/(-z + 1);
dshapes(9,2) = -2*z*(-2*x - 2*z + 2)/(-z + 1) - 2*z*(-2*y - 2*z + 2)/(-z + 1) + z*(-2*x - 2*z + 2)*(-2*y - 2*z + 2)/((-z + 1)*(-z + 1)) + (-2*x - 2*z + 2)*(-2*y - 2*z + 2)/(-z + 1);
dshapes(10,0) = 2*z*(-2*y - 2*z + 2)/(-z + 1);
dshapes(10,1) = -4*x*z/(-z + 1);
dshapes(10,2) = -4*x*z/(-z + 1) + 2*x*z*(-2*y - 2*z + 2)/((-z + 1)*(-z + 1)) + 2*x*(-2*y - 2*z + 2)/(-z + 1);
dshapes(11,0) = 4*y*z/(-z + 1);
dshapes(11,1) = 4*x*z/(-z + 1);
dshapes(11,2) = 4*x*y*z/((-z + 1)*(-z + 1)) + 4*x*y/(-z + 1);
dshapes(12,0) = -4*y*z/(-z + 1);
dshapes(12,1) = 2*z*(-2*x - 2*z + 2)/(-z + 1);
dshapes(12,2) = -4*y*z/(-z + 1) + 2*y*z*(-2*x - 2*z + 2)/((-z + 1)*(-z + 1)) + 2*y*(-2*x - 2*z + 2)/(-z + 1);
break;
}
case HEX:
{
// if (typeid(T) == typeid(SIMD<double>)) return;
// NgProfiler::StartTimer(timer);
T x = xi(0);
T y = xi(1);
T z = xi(2);
// shapes[0] = (1-x)*(1-y)*(1-z);
dshapes(0,0) = - (1-y)*(1-z);
dshapes(0,1) = (1-x) * (-1) * (1-z);
dshapes(0,2) = (1-x) * (1-y) * (-1);
// shapes[1] = x *(1-y)*(1-z);
dshapes(1,0) = (1-y)*(1-z);
dshapes(1,1) = -x * (1-z);
dshapes(1,2) = -x * (1-y);
// shapes[2] = x * y *(1-z);
dshapes(2,0) = y * (1-z);
dshapes(2,1) = x * (1-z);
dshapes(2,2) = -x * y;
// shapes[3] = (1-x)* y *(1-z);
dshapes(3,0) = -y * (1-z);
dshapes(3,1) = (1-x) * (1-z);
dshapes(3,2) = -(1-x) * y;
// shapes[4] = (1-x)*(1-y)*z;
dshapes(4,0) = - (1-y)*z;
dshapes(4,1) = (1-x) * (-1) * z;
dshapes(4,2) = (1-x) * (1-y) * 1;
// shapes[5] = x *(1-y)*z;
dshapes(5,0) = (1-y)*z;
dshapes(5,1) = -x * z;
dshapes(5,2) = x * (1-y);
// shapes[6] = x * y *z;
dshapes(6,0) = y * z;
dshapes(6,1) = x * z;
dshapes(6,2) = x * y;
// shapes[7] = (1-x)* y *z;
dshapes(7,0) = -y * z;
dshapes(7,1) = (1-x) * z;
dshapes(7,2) = (1-x) * y;
// NgProfiler::StopTimer(timer);
if (info.order == 1) return;
T shapes[8] = {
(1-x)*(1-y)*(1-z),
x *(1-y)*(1-z),
x * y *(1-z),
(1-x)* y *(1-z),
(1-x)*(1-y)*(z),
x *(1-y)*(z),
x * y *(z),
(1-x)* y *(z),
};
T mu[8] = {
(1-x)+(1-y)+(1-z),
x +(1-y)+(1-z),
x + y +(1-z),
(1-x)+ y +(1-z),
(1-x)+(1-y)+(z),
x +(1-y)+(z),
x + y +(z),
(1-x)+ y +(z)
};
T dmu[8][3] = {
{ -1, -1, -1 },
{ 1, -1, -1 },
{ 1, 1, -1 },
{ -1, 1, -1 },
{ -1, -1, 1 },
{ 1, -1, 1 },
{ 1, 1, 1 },
{ -1, 1, 1 }
};
NgArrayMem<T, 20> hshapes(order+1), hdshapes(order+1);
int ii = 8;
const ELEMENT_EDGE * edges = MeshTopology::GetEdges1 (HEX);
for (int i = 0; i < 12; i++)
{
int eorder = edgeorder[info.edgenrs[i]];
if (eorder >= 2)
{
int vi1 = edges[i][0]-1, vi2 = edges[i][1]-1;
if (el[vi1] > el[vi2]) swap (vi1, vi2);
CalcEdgeShapeDx (eorder, mu[vi1]-mu[vi2], &hshapes[0], &hdshapes[0]);
T lame = shapes[vi1]+shapes[vi2];
T dlame[3] = {
dshapes(vi1, 0) + dshapes(vi2, 0),
dshapes(vi1, 1) + dshapes(vi2, 1),
dshapes(vi1, 2) + dshapes(vi2, 2)
};
for (int j = 0; j < eorder-1; j++)
for (int k = 0; k < 3; k++)
dshapes(ii+j, k) =
lame * hdshapes[j] * (dmu[vi1][k]-dmu[vi2][k])
+ dlame[k] * hshapes[j];
ii += eorder-1;
}
}
/*
*testout << "quad, dshape = " << endl << dshapes << endl;
for (int i = 0; i < 2; i++)
{
Point<2> xil = xi, xir = xi;
Vector shapesl(dshapes.Height()), shapesr(dshapes.Height());
xil(i) -= 1e-6;
xir(i) += 1e-6;
CalcElementShapes (info, xil, shapesl);
CalcElementShapes (info, xir, shapesr);
for (int j = 0; j < dshapes.Height(); j++)
dshapes(j,i) = 1.0 / 2e-6 * (shapesr(j)-shapesl(j));
}
*testout << "quad, num dshape = " << endl << dshapes << endl;
*/
break;
}
case HEX20:
{
AutoDiff<3,T> x(xi(0), 0);
AutoDiff<3,T> y(xi(1), 1);
AutoDiff<3,T> z(xi(2), 2);
AutoDiff<3,T> ad[20];
ad[0] = (1-x)*(1-y)*(1-z);
ad[1] = x *(1-y)*(1-z);
ad[2] = x * y *(1-z);
ad[3] = (1-x)* y *(1-z);
ad[4] = (1-x)*(1-y)*(z);
ad[5] = x *(1-y)*(z);
ad[6] = x * y *(z);
ad[7] = (1-x)* y *(z);
AutoDiff<3,T> sigma[8]={(1-x)+(1-y)+(1-z),x+(1-y)+(1-z),x+y+(1-z),(1-x)+y+(1-z),
(1-x)+(1-y)+z,x+(1-y)+z,x+y+z,(1-x)+y+z};
static const int e[12][2] =
{
{ 0, 1 }, { 2, 3 }, { 3, 0 }, { 1, 2 },
{ 4, 5 }, { 6, 7 }, { 7, 4 }, { 5, 6 },
{ 0, 4 }, { 1, 5 }, { 2, 6 }, { 3, 7 },
};
for (int i = 0; i < 12; i++)
{
auto lame = ad[e[i][0]]+ad[e[i][1]];
auto xi = sigma[e[i][1]]-sigma[e[i][0]];
ad[8+i] = (1-xi*xi)*lame;
}
for (int i = 0; i < 12; i++)
{
ad[e[i][0]] -= 0.5 * ad[8+i];
ad[e[i][1]] -= 0.5 * ad[8+i];
}
for (int i = 0; i < 20; i++)
for (int j = 0; j < 3; j++)
dshapes(i,j) = ad[i].DValue(j);
break;
}
default:
throw NgException("CurvedElements::CalcDShape 3d, element type not handled");
}
/*
DenseMatrix dshapes2 (info.ndof, 3);
Vector shapesl(info.ndof);
Vector shapesr(info.ndof);
double eps = 1e-6;
for (int i = 0; i < 3; i++)
{
Point<3> xl = xi;
Point<3> xr = xi;
xl(i) -= eps;
xr(i) += eps;
CalcElementShapes (info, xl, shapesl);
CalcElementShapes (info, xr, shapesr);
for (int j = 0; j < info.ndof; j++)
dshapes2(j,i) = (shapesr(j)-shapesl(j)) / (2*eps);
}
(*testout) << "dshapes = " << endl << dshapes << endl;
(*testout) << "dshapes2 = " << endl << dshapes2 << endl;
dshapes2 -= dshapes;
(*testout) << "diff = " << endl << dshapes2 << endl;
*/
}
// extern int mappingvar;
template <typename T>
bool CurvedElements ::
EvaluateMapping (ElementInfo & info, Point<3,T> xi, Point<3,T> & mx, Mat<3,3,T> & jac) const
{
const Element & el = mesh[info.elnr];
if (rational && info.order >= 2) return false; // not supported
AutoDiff<3,T> x(xi(0), 0);
AutoDiff<3,T> y(xi(1), 1);
AutoDiff<3,T> z(xi(2), 2);
AutoDiff<3,T> mapped_x[3] = { T(0.0), T(0.0), T(0.0) } ;
switch (el.GetType())
{
case TET:
{
// if (info.order >= 2) return false; // not yet supported
AutoDiff<3,T> lami[4] = { x, y, z, 1-x-y-z };
for (int j = 0; j < 4; j++)
{
Point<3> p = mesh[el[j]];
for (int k = 0; k < 3; k++)
mapped_x[k] += p(k) * lami[j];
}
if (info.order == 1) break;
const ELEMENT_EDGE * edges = MeshTopology::GetEdges1 (TET);
for (int i = 0; i < 6; i++)
{
int eorder = edgeorder[info.edgenrs[i]];
if (eorder >= 2)
{
int first = edgecoeffsindex[info.edgenrs[i]];
int vi1 = edges[i][0]-1, vi2 = edges[i][1]-1;
if (el[vi1] > el[vi2]) swap (vi1, vi2);
CalcScaledEdgeShapeLambda (eorder, lami[vi1]-lami[vi2], lami[vi1]+lami[vi2],
[&](int i, AutoDiff<3,T> shape)
{
Vec<3> coef = edgecoeffs[first+i];
for (int k = 0; k < 3; k++)
mapped_x[k] += coef(k) * shape;
});
}
}
const ELEMENT_FACE * faces = MeshTopology::GetFaces1 (TET);
for (int i = 0; i < 4; i++)
{
int forder = faceorder[info.facenrs[i]];
if (forder >= 3)
{
int first = facecoeffsindex[info.facenrs[i]];
int fnums[] = { faces[i][0]-1, faces[i][1]-1, faces[i][2]-1 };
if (el[fnums[0]] > el[fnums[1]]) swap (fnums[0], fnums[1]);
if (el[fnums[1]] > el[fnums[2]]) swap (fnums[1], fnums[2]);
if (el[fnums[0]] > el[fnums[1]]) swap (fnums[0], fnums[1]);
CalcScaledTrigShapeLambda (forder,
lami[fnums[1]]-lami[fnums[0]], lami[fnums[2]],
lami[fnums[0]]+lami[fnums[1]]+lami[fnums[2]],
[&](int i, AutoDiff<3,T> shape)
{
Vec<3> coef = facecoeffs[first+i];
for (int k = 0; k < 3; k++)
mapped_x[k] += coef(k) * shape;
});
}
}
break;
}
case HEX:
{
if (info.order >= 2) return false; // not yet supported
AutoDiff<3,T> lami[8] =
{ (1-x)*(1-y)*(1-z),
( x)*(1-y)*(1-z),
( x)* y *(1-z),
(1-x)* y *(1-z),
(1-x)*(1-y)*(z),
( x)*(1-y)*(z),
( x)* y *(z),
(1-x)* y *(z) };
for (int j = 0; j < 8; j++)
{
Point<3> p = mesh[el[j]];
for (int k = 0; k < 3; k++)
mapped_x[k] += p(k) * lami[j];
}
if (info.order == 1) break;
AutoDiff<3,T> mu[8] = {
(1-x)+(1-y)+(1-z),
x +(1-y)+(1-z),
x + y +(1-z),
(1-x)+ y +(1-z),
(1-x)+(1-y)+(z),
x +(1-y)+(z),
x + y +(z),
(1-x)+ y +(z),
};
// int ii = 8;
const ELEMENT_EDGE * edges = MeshTopology::GetEdges1 (HEX);
for (int i = 0; i < 12; i++)
{
int eorder = edgeorder[info.edgenrs[i]];
if (eorder >= 2)
{
int first = edgecoeffsindex[info.edgenrs[i]];
int vi1 = edges[i][0]-1, vi2 = edges[i][1]-1;
if (el[vi1] > el[vi2]) swap (vi1, vi2);
AutoDiff<3,T> lame = lami[vi1]+lami[vi2];
CalcEdgeShapeLambda (eorder, mu[vi1]-mu[vi2],
[&](int i, AutoDiff<3,T> shape)
{
Vec<3> coef = edgecoeffs[first+i];
for (int k = 0; k < 3; k++)
mapped_x[k] += coef(k) * (lame*shape);
});
}
}
break;
}
default:
return false;
}
for (int i = 0; i < 3; i++)
{
mx(i) = mapped_x[i].Value();
for (int j = 0; j < 3; j++)
jac(i,j) = mapped_x[i].DValue(j);
}
return true;
}
void CurvedElements ::
GetCoefficients (ElementInfo & info, Vec<3> * coefs) const
{
const Element & el = mesh[info.elnr];
for (int i = 0; i < info.nv; i++)
coefs[i] = Vec<3> (mesh[el[i]]);
if (info.order == 1) return;
int ii = info.nv;
for (int i = 0; i < info.nedges; i++)
{
int first = edgecoeffsindex[info.edgenrs[i]];
int next = edgecoeffsindex[info.edgenrs[i]+1];
for (int j = first; j < next; j++, ii++)
coefs[ii] = edgecoeffs[j];
}
for (int i = 0; i < info.nfaces; i++)
{
int first = facecoeffsindex[info.facenrs[i]];
int next = facecoeffsindex[info.facenrs[i]+1];
for (int j = first; j < next; j++, ii++)
coefs[ii] = facecoeffs[j];
}
}
/*
void CurvedElements ::
CalcMultiPointSegmentTransformation (NgArray<double> * xi, SegmentIndex segnr,
NgArray<Point<3> > * x,
NgArray<Vec<3> > * dxdxi)
{
;
}
*/
template <int DIM_SPACE, typename T>
void CurvedElements ::
CalcMultiPointSegmentTransformation (SegmentIndex elnr, int n,
const T * xi, size_t sxi,
T * x, size_t sx,
T * dxdxi, size_t sdxdxi)
{
for (int ip = 0; ip < n; ip++)
{
Point<3,T> xg;
Vec<3,T> dx;
// mesh->GetCurvedElements().
CalcSegmentTransformation<T> (xi[ip*sxi], elnr, &xg, &dx);
if (x)
for (int i = 0; i < DIM_SPACE; i++)
x[ip*sx+i] = xg(i);
if (dxdxi)
for (int i=0; i<DIM_SPACE; i++)
dxdxi[ip*sdxdxi+i] = dx(i);
}
}
template void CurvedElements ::
CalcMultiPointSegmentTransformation<2> (SegmentIndex elnr, int npts,
const double * xi, size_t sxi,
double * x, size_t sx,
double * dxdxi, size_t sdxdxi);
template void CurvedElements ::
CalcMultiPointSegmentTransformation<3> (SegmentIndex elnr, int npts,
const double * xi, size_t sxi,
double * x, size_t sx,
double * dxdxi, size_t sdxdxi);
template void CurvedElements ::
CalcMultiPointSegmentTransformation<2> (SegmentIndex elnr, int npts,
const SIMD<double> * xi, size_t sxi,
SIMD<double> * x, size_t sx,
SIMD<double> * dxdxi, size_t sdxdxi);
template void CurvedElements ::
CalcMultiPointSegmentTransformation<3> (SegmentIndex elnr, int npts,
const SIMD<double> * xi, size_t sxi,
SIMD<double> * x, size_t sx,
SIMD<double> * dxdxi, size_t sdxdxi);
template void CurvedElements ::
CalcSegmentTransformation<double> (const double & xi, SegmentIndex elnr,
Point<3,double> * x, Vec<3,double> * dxdxi, bool * curved);
void CurvedElements ::
CalcMultiPointSurfaceTransformation (NgArray< Point<2> > * xi, SurfaceElementIndex elnr,
NgArray< Point<3> > * x,
NgArray< Mat<3,2> > * dxdxi)
{
double * px = (x) ? &(*x)[0](0) : NULL;
double * pdxdxi = (dxdxi) ? &(*dxdxi)[0](0) : NULL;
CalcMultiPointSurfaceTransformation <3> (elnr, xi->Size(),
&(*xi)[0](0), 2,
px, 3,
pdxdxi, 6);
}
template <int DIM_SPACE, typename T>
void CurvedElements ::
CalcMultiPointSurfaceTransformation (SurfaceElementIndex elnr, int npts,
const T * xi, size_t sxi,
T * x, size_t sx,
T * dxdxi, size_t sdxdxi)
{
if (mesh.coarsemesh)
{
const HPRefElement & hpref_el =
(*mesh.hpelements) [mesh[elnr].hp_elnr];
// xi umrechnen
T lami[4];
TFlatVector<T> vlami(4, lami);
NgArrayMem<Point<2,T>, 50> coarse_xi (npts);
for (int pi = 0; pi < npts; pi++)
{
vlami = 0;
Point<2,T> hxi(xi[pi*sxi], xi[pi*sxi+1]);
mesh[elnr].GetShapeNew ( hxi, vlami);
Point<2,T> cxi(0,0);
for (int i = 0; i < hpref_el.np; i++)
for (int j = 0; j < 2; j++)
cxi(j) += hpref_el.param[i][j] * lami[i];
coarse_xi[pi] = cxi;
}
mesh.coarsemesh->GetCurvedElements().
CalcMultiPointSurfaceTransformation<DIM_SPACE,T> (hpref_el.coarse_elnr, npts,
&coarse_xi[0](0), &coarse_xi[1](0)-&coarse_xi[0](0),
x, sx, dxdxi, sdxdxi);
// Mat<3,2> dxdxic;
if (dxdxi)
{
T mem_dlami[8]; // avoid alignment problems if T is SIMD
MatrixFixWidth<2,T> dlami(4, mem_dlami);
dlami = T(0.0);
for (int pi = 0; pi < npts; pi++)
{
Point<2,T> hxi(xi[pi*sxi], xi[pi*sxi+1]);
mesh[elnr].GetDShapeNew ( hxi, dlami);
Mat<2,2,T> trans;
trans = 0;
for (int k = 0; k < 2; k++)
for (int l = 0; l < 2; l++)
for (int i = 0; i < hpref_el.np; i++)
trans(l,k) += hpref_el.param[i][l] * dlami(i, k);
Mat<DIM_SPACE,2,T> hdxdxic, hdxdxi;
for (int k = 0; k < 2*DIM_SPACE; k++)
hdxdxic(k) = dxdxi[pi*sdxdxi+k];
hdxdxi = hdxdxic * trans;
for (int k = 0; k < 2*DIM_SPACE; k++)
dxdxi[pi*sdxdxi+k] = hdxdxi(k);
// dxdxic = (*dxdxi)[pi];
// (*dxdxi)[pi] = dxdxic * trans;
}
}
return;
}
const Element2d & el = mesh[elnr];
ELEMENT_TYPE type = el.GetType();
SurfaceElementInfo info;
info.elnr = elnr;
info.order = order;
switch (type)
{
case TRIG : info.nv = 3; break;
case QUAD : info.nv = 4; break;
case TRIG6: info.nv = 6; break;
case QUAD8 : info.nv = 8; break;
default:
cerr << "undef element in CalcMultPointSurfaceTrafo" << endl;
}
info.ndof = info.nv;
// if (info.order > 1)
// {
// const MeshTopology & top = mesh.GetTopology();
// top.GetSurfaceElementEdges (elnr+1, info.edgenrs);
// for (int i = 0; i < info.edgenrs.Size(); i++)
// info.edgenrs[i]--;
// info.facenr = top.GetSurfaceElementFace (elnr+1)-1;
// for (int i = 0; i < info.edgenrs.Size(); i++)
// info.ndof += edgecoeffsindex[info.edgenrs[i]+1] - edgecoeffsindex[info.edgenrs[i]];
// info.ndof += facecoeffsindex[info.facenr+1] - facecoeffsindex[info.facenr];
// }
// Michael Woopen: THESE FOLLOWING LINES ARE COPIED FROM CurvedElements::CalcSurfaceTransformation
if (info.order > 1)
{
const MeshTopology & top = mesh.GetTopology();
top.GetSurfaceElementEdges (elnr+1, info.edgenrs);
for (int i = 0; i < info.edgenrs.Size(); i++)
info.edgenrs[i]--;
info.facenr = top.GetSurfaceElementFace (elnr+1)-1;
bool firsttry = true;
bool problem = false;
while(firsttry || problem)
{
problem = false;
for (int i = 0; !problem && i < info.edgenrs.Size(); i++)
{
if(info.edgenrs[i]+1 >= edgecoeffsindex.Size())
problem = true;
else
info.ndof += edgecoeffsindex[info.edgenrs[i]+1] - edgecoeffsindex[info.edgenrs[i]];
}
if(info.facenr+1 >= facecoeffsindex.Size())
problem = true;
else
info.ndof += facecoeffsindex[info.facenr+1] - facecoeffsindex[info.facenr];
if(problem && !firsttry)
throw NgException("something wrong with curved elements");
if(problem)
BuildCurvedElements(NULL,order,rational);
firsttry = false;
}
}
bool ok = true;
for (int i = 0; i < npts; i++)
{
Point<2,T> _xi(xi[i*sxi], xi[i*sxi+1]);
Point<DIM_SPACE,T> _x;
Mat<DIM_SPACE,2,T> _dxdxi;
if (!EvaluateMapping (info, _xi, _x, _dxdxi))
{ ok = false; break; }
// *testout << "x = " << _x << ", dxdxi = " << _dxdxi << endl;
if (x)
for (int j = 0; j < DIM_SPACE; j++)
x[i*sx+j] = _x[j];
if (dxdxi)
for (int j = 0; j < DIM_SPACE; j++)
for (int k = 0; k < 2; k++)
dxdxi[i*sdxdxi+2*j+k] = _dxdxi(j,k);
}
if (ok) return;
// THESE LAST LINES ARE COPIED FROM CurvedElements::CalcSurfaceTransformation
NgArrayMem<Vec<DIM_SPACE>,100> coefs(info.ndof);
GetCoefficients (info, coefs);
NgArrayMem<T, 100> shapes_mem(info.ndof);
TFlatVector<T> shapes(info.ndof, &shapes_mem[0]);
NgArrayMem<T, 100> dshapes_mem(info.ndof*2);
MatrixFixWidth<2,T> dshapes(info.ndof,&shapes_mem[0]);
if (x)
{
if (info.order == 1 && type == TRIG)
{
for (int j = 0; j < npts; j++)
{
Point<2,T> vxi(xi[j*sxi], xi[j*sxi+1]);
Point<DIM_SPACE,T> val;
for (int k = 0; k < DIM_SPACE; k++)
val(k) = coefs[2](k) + (coefs[0](k)-coefs[2](k)) * vxi(0) + (coefs[1](k)-coefs[2](k)) * vxi(1);
/*
(coefs[2]);
val += (coefs[0]-coefs[2]) * vxi(0);
val += (coefs[1]-coefs[2]) * vxi(1);
*/
for (int k = 0; k < DIM_SPACE; k++)
x[j*sx+k] = val(k);
}
}
else
for (int j = 0; j < npts; j++)
{
Point<2,T> vxi(xi[j*sxi], xi[j*sxi+1]);
CalcElementShapes (info, vxi, shapes);
Point<DIM_SPACE,T> val = T(0.0);
for (int i = 0; i < coefs.Size(); i++)
for (int k = 0; k < DIM_SPACE; k++)
val(k) += shapes(i) * coefs[i](k);
for (int k = 0; k < DIM_SPACE; k++)
x[j*sx+k] = val(k);
}
}
if (dxdxi)
{
if (info.order == 1 && type == TRIG)
{
Point<2,T> xij(xi[0], xi[1]);
CalcElementDShapes (info, xij, dshapes);
Mat<3,2,T> dxdxij;
dxdxij = 0.0;
for (int i = 0; i < coefs.Size(); i++)
for (int j = 0; j < DIM_SPACE; j++)
for (int k = 0; k < 2; k++)
dxdxij(j,k) += dshapes(i,k) * coefs[i](j);
for (int ip = 0; ip < npts; ip++)
for (int j = 0; j < DIM_SPACE; j++)
for (int k = 0; k < 2; k++)
dxdxi[ip*sdxdxi+2*j+k] = dxdxij(j,k);
}
else
{
for (int j = 0; j < npts; j++)
{
Point<2,T> vxi(xi[j*sxi], xi[j*sxi+1]);
CalcElementDShapes (info, vxi, dshapes);
Mat<DIM_SPACE,2,T> ds;
ds = 0.0;
for (int i = 0; i < coefs.Size(); i++)
for (int j = 0; j < DIM_SPACE; j++)
for (int k = 0; k < 2; k++)
ds(j,k) += dshapes(i,k) * coefs[i](j);
// (*dxdxi)[ip] = ds;
for (int k = 0; k < 2*DIM_SPACE; k++)
dxdxi[j*sdxdxi+k] = ds(k);
}
}
}
}
template void CurvedElements ::
CalcMultiPointSurfaceTransformation<2> (SurfaceElementIndex elnr, int npts,
const double * xi, size_t sxi,
double * x, size_t sx,
double * dxdxi, size_t sdxdxi);
template void CurvedElements ::
CalcMultiPointSurfaceTransformation<3> (SurfaceElementIndex elnr, int npts,
const double * xi, size_t sxi,
double * x, size_t sx,
double * dxdxi, size_t sdxdxi);
template void CurvedElements ::
CalcMultiPointSurfaceTransformation<2> (SurfaceElementIndex elnr, int npts,
const SIMD<double> * xi, size_t sxi,
SIMD<double> * x, size_t sx,
SIMD<double> * dxdxi, size_t sdxdxi);
template void CurvedElements ::
CalcMultiPointSurfaceTransformation<3> (SurfaceElementIndex elnr, int npts,
const SIMD<double> * xi, size_t sxi,
SIMD<double> * x, size_t sx,
SIMD<double> * dxdxi, size_t sdxdxi);
void CurvedElements ::
CalcMultiPointElementTransformation (NgArray< Point<3> > * xi, ElementIndex elnr,
NgArray< Point<3> > * x,
NgArray< Mat<3,3> > * dxdxi)
{
double * px = (x) ? &(*x)[0](0) : NULL;
double * pdxdxi = (dxdxi) ? &(*dxdxi)[0](0) : NULL;
CalcMultiPointElementTransformation (elnr, xi->Size(),
&(*xi)[0](0), 3,
px, 3,
pdxdxi, 9);
return;
#ifdef OLD
if (mesh.coarsemesh)
{
const HPRefElement & hpref_el =
(*mesh.hpelements) [mesh[elnr].hp_elnr];
// xi umrechnen
double lami[8];
FlatVector vlami(8, lami);
NgArrayMem<Point<3>, 50> coarse_xi (xi->Size());
for (int pi = 0; pi < xi->Size(); pi++)
{
vlami = 0;
mesh[elnr].GetShapeNew ( (*xi)[pi], vlami);
Point<3> cxi(0,0,0);
for (int i = 0; i < hpref_el.np; i++)
for (int j = 0; j < 3; j++)
cxi(j) += hpref_el.param[i][j] * lami[i];
coarse_xi[pi] = cxi;
}
mesh.coarsemesh->GetCurvedElements().
CalcMultiPointElementTransformation (&coarse_xi, hpref_el.coarse_elnr, x, dxdxi);
Mat<3,3> trans, dxdxic;
if (dxdxi)
{
MatrixFixWidth<3> dlami(8);
dlami = 0;
for (int pi = 0; pi < xi->Size(); pi++)
{
mesh[elnr].GetDShapeNew ( (*xi)[pi], dlami);
trans = 0;
for (int k = 0; k < 3; k++)
for (int l = 0; l < 3; l++)
for (int i = 0; i < hpref_el.np; i++)
trans(l,k) += hpref_el.param[i][l] * dlami(i, k);
dxdxic = (*dxdxi)[pi];
(*dxdxi)[pi] = dxdxic * trans;
}
}
return;
}
Vector shapes;
MatrixFixWidth<3> dshapes;
const Element & el = mesh[elnr];
ELEMENT_TYPE type = el.GetType();
ElementInfo info;
info.elnr = elnr;
info.order = order;
info.ndof = info.nv = MeshTopology::GetNPoints (type);
if (info.order > 1)
{
const MeshTopology & top = mesh.GetTopology();
info.nedges = top.GetElementEdges (elnr+1, info.edgenrs, 0);
for (int i = 0; i < info.nedges; i++)
info.edgenrs[i]--;
info.nfaces = top.GetElementFaces (elnr+1, info.facenrs, 0);
for (int i = 0; i < info.nfaces; i++)
info.facenrs[i]--;
for (int i = 0; i < info.nedges; i++)
info.ndof += edgecoeffsindex[info.edgenrs[i]+1] - edgecoeffsindex[info.edgenrs[i]];
for (int i = 0; i < info.nfaces; i++)
info.ndof += facecoeffsindex[info.facenrs[i]+1] - facecoeffsindex[info.facenrs[i]];
// info.ndof += facecoeffsindex[info.facenr+1] - facecoeffsindex[info.facenr];
}
NgArray<Vec<3> > coefs(info.ndof);
GetCoefficients (info, &coefs[0]);
if (x)
{
for (int j = 0; j < xi->Size(); j++)
{
CalcElementShapes (info, (*xi)[j], shapes);
(*x)[j] = 0;
for (int i = 0; i < coefs.Size(); i++)
(*x)[j] += shapes(i) * coefs[i];
}
}
if (dxdxi)
{
if (info.order == 1 && type == TET)
{
if (xi->Size() > 0)
{
CalcElementDShapes (info, (*xi)[0], dshapes);
Mat<3,3> ds;
ds = 0;
for (int i = 0; i < coefs.Size(); i++)
for (int j = 0; j < 3; j++)
for (int k = 0; k < 3; k++)
ds(j,k) += dshapes(i,k) * coefs[i](j);
for (int ip = 0; ip < xi->Size(); ip++)
(*dxdxi)[ip] = ds;
}
}
else
for (int ip = 0; ip < xi->Size(); ip++)
{
CalcElementDShapes (info, (*xi)[ip], dshapes);
Mat<3,3> ds;
ds = 0;
for (int i = 0; i < coefs.Size(); i++)
for (int j = 0; j < 3; j++)
for (int k = 0; k < 3; k++)
ds(j,k) += dshapes(i,k) * coefs[i](j);
(*dxdxi)[ip] = ds;
}
}
#endif
}
// extern int multipointtrafovar;
template <typename T>
void CurvedElements ::
CalcMultiPointElementTransformation (ElementIndex elnr, int n,
const T * xi, size_t sxi,
T * x, size_t sx,
T * dxdxi, size_t sdxdxi)
{
// multipointtrafovar++;
/*
static int timer = NgProfiler::CreateTimer ("calcmultipointelementtrafo");
static int timer1 = NgProfiler::CreateTimer ("calcmultipointelementtrafo 1");
static int timer2 = NgProfiler::CreateTimer ("calcmultipointelementtrafo 2");
static int timer3 = NgProfiler::CreateTimer ("calcmultipointelementtrafo 3");
static int timer4 = NgProfiler::CreateTimer ("calcmultipointelementtrafo 4");
static int timer5 = NgProfiler::CreateTimer ("calcmultipointelementtrafo 5");
NgProfiler::RegionTimer reg(timer);
*/
// NgProfiler::StartTimer (timer);
// NgProfiler::StartTimer (timer1);
if (mesh.coarsemesh)
{
const HPRefElement & hpref_el =
(*mesh.hpelements) [mesh[elnr].hp_elnr];
// xi umrechnen
T lami[8];
TFlatVector<T> vlami(8, &lami[0]);
NgArrayMem<T, 100> coarse_xi (3*n);
for (int pi = 0; pi < n; pi++)
{
vlami = 0;
Point<3,T> pxi;
for (int j = 0; j < 3; j++)
pxi(j) = xi[pi*sxi+j];
mesh[elnr].GetShapeNew (pxi, vlami);
Point<3,T> cxi(0,0,0);
for (int i = 0; i < hpref_el.np; i++)
for (int j = 0; j < 3; j++)
cxi(j) += hpref_el.param[i][j] * lami[i];
for (int j = 0; j < 3; j++)
coarse_xi[3*pi+j] = cxi(j);
}
mesh.coarsemesh->GetCurvedElements().
CalcMultiPointElementTransformation (hpref_el.coarse_elnr, n,
&coarse_xi[0], 3,
x, sx,
dxdxi, sdxdxi);
Mat<3,3,T> trans, dxdxic;
if (dxdxi)
{
MatrixFixWidth<3,T> dlami(8);
dlami = T(0);
for (int pi = 0; pi < n; pi++)
{
Point<3,T> pxi;
for (int j = 0; j < 3; j++)
pxi(j) = xi[pi*sxi+j];
mesh[elnr].GetDShapeNew (pxi, dlami);
trans = 0;
for (int k = 0; k < 3; k++)
for (int l = 0; l < 3; l++)
for (int i = 0; i < hpref_el.np; i++)
trans(l,k) += hpref_el.param[i][l] * dlami(i, k);
Mat<3,3,T> mat_dxdxic, mat_dxdxi;
for (int j = 0; j < 3; j++)
for (int k = 0; k < 3; k++)
mat_dxdxic(j,k) = dxdxi[pi*sdxdxi+3*j+k];
mat_dxdxi = mat_dxdxic * trans;
for (int j = 0; j < 3; j++)
for (int k = 0; k < 3; k++)
dxdxi[pi*sdxdxi+3*j+k] = mat_dxdxi(j,k);
// dxdxic = (*dxdxi)[pi];
// (*dxdxi)[pi] = dxdxic * trans;
}
}
return;
}
// NgProfiler::StopTimer (timer1);
// NgProfiler::StartTimer (timer2);
const Element & el = mesh[elnr];
ELEMENT_TYPE type = el.GetType();
ElementInfo info;
info.elnr = elnr;
info.order = order;
info.ndof = info.nv = MeshTopology::GetNPoints (type);
if (info.order > 1)
{
const MeshTopology & top = mesh.GetTopology();
info.nedges = top.GetElementEdges (elnr+1, info.edgenrs, 0);
for (int i = 0; i < info.nedges; i++)
info.edgenrs[i]--;
info.nfaces = top.GetElementFaces (elnr+1, info.facenrs, 0);
for (int i = 0; i < info.nfaces; i++)
info.facenrs[i]--;
for (int i = 0; i < info.nedges; i++)
info.ndof += edgecoeffsindex[info.edgenrs[i]+1] - edgecoeffsindex[info.edgenrs[i]];
for (int i = 0; i < info.nfaces; i++)
info.ndof += facecoeffsindex[info.facenrs[i]+1] - facecoeffsindex[info.facenrs[i]];
// info.ndof += facecoeffsindex[info.facenr+1] - facecoeffsindex[info.facenr];
}
// NgProfiler::StopTimer (timer2);
// NgProfiler::StartTimer (timer3);
bool ok = true;
for (int i = 0; i < n; i++)
{
Point<3,T> _xi(xi[i*sxi], xi[i*sxi+1], xi[i*sxi+2]);
Point<3,T> _x;
Mat<3,3,T> _dxdxi;
if (!EvaluateMapping (info, _xi, _x, _dxdxi))
{ ok = false; break; }
// cout << "x = " << _x << ", dxdxi = " << _dxdxi << endl;
if (x)
for (int j = 0; j < 3; j++)
x[i*sx+j] = _x[j];
if (dxdxi)
for (int j = 0; j < 3; j++)
for (int k = 0; k < 3; k++)
dxdxi[i*sdxdxi+3*j+k] = _dxdxi(j,k);
}
if (ok) return;
NgArrayMem<Vec<3>,100> coefs(info.ndof);
NgArrayMem<T,500> shapes_mem(info.ndof);
TFlatVector<T> shapes(info.ndof, &shapes_mem[0]);
NgArrayMem<T,1500> dshapes_mem(3*info.ndof);
MatrixFixWidth<3,T> dshapes(info.ndof, &dshapes_mem[0]);
// NgProfiler::StopTimer (timer3);
// NgProfiler::StartTimer (timer4);
GetCoefficients (info, &coefs[0]);
if (x)
{
for (int j = 0; j < n; j++)
{
Point<3,T> xij, xj;
for (int k = 0; k < 3; k++)
xij(k) = xi[j*sxi+k];
CalcElementShapes (info, xij, shapes);
xj = T(0.0);
for (int i = 0; i < coefs.Size(); i++)
for (int k = 0; k < 3; k++)
xj(k) += shapes(i) * coefs[i](k);
// cout << "old, xj = " << xj << endl;
for (int k = 0; k < 3; k++)
x[j*sx+k] = xj(k);
}
}
// NgProfiler::StopTimer (timer4);
// NgProfiler::StartTimer (timer5);
if (dxdxi)
{
if (info.order == 1 && type == TET)
{
if (n > 0)
{
Point<3,T> xij;
for (int k = 0; k < 3; k++)
xij(k) = xi[k];
CalcElementDShapes (info, xij, dshapes);
Mat<3,3,T> dxdxij;
dxdxij = 0.0;
for (int i = 0; i < coefs.Size(); i++)
for (int j = 0; j < 3; j++)
for (int k = 0; k < 3; k++)
dxdxij(j,k) += dshapes(i,k) * coefs[i](j);
for (int ip = 0; ip < n; ip++)
for (int j = 0; j < 3; j++)
for (int k = 0; k < 3; k++)
dxdxi[ip*sdxdxi+3*j+k] = dxdxij(j,k);
}
}
else
{
for (int ip = 0; ip < n; ip++)
{
Point<3,T> xij;
for (int k = 0; k < 3; k++)
xij(k) = xi[ip*sxi+k];
CalcElementDShapes (info, xij, dshapes);
Mat<3,3,T> dxdxij;
dxdxij = 0.0;
for (int i = 0; i < coefs.Size(); i++)
for (int j = 0; j < 3; j++)
for (int k = 0; k < 3; k++)
dxdxij(j,k) += dshapes(i,k) * coefs[i](j);
// cout << "old, jac = " << dxdxij << endl;
for (int j = 0; j < 3; j++)
for (int k = 0; k < 3; k++)
dxdxi[ip*sdxdxi+3*j+k] = dxdxij(j,k);
/*
T dxdxi00 = T(0.0);
T dxdxi01 = T(0.0);
T dxdxi02 = T(0.0);
T dxdxi10 = T(0.0);
T dxdxi11 = T(0.0);
T dxdxi12 = T(0.0);
T dxdxi20 = T(0.0);
T dxdxi21 = T(0.0);
T dxdxi22 = T(0.0);
for (int i = 0; i < coefs.Size(); i++)
{
T ds0 = dshapes(i,0);
T ds1 = dshapes(i,1);
T ds2 = dshapes(i,2);
T cf0 = coefs[i](0);
T cf1 = coefs[i](1);
T cf2 = coefs[i](2);
dxdxi00 += ds0*cf0;
dxdxi01 += ds1*cf0;
dxdxi02 += ds2*cf0;
dxdxi10 += ds0*cf1;
dxdxi11 += ds1*cf1;
dxdxi12 += ds2*cf1;
dxdxi20 += ds0*cf2;
dxdxi21 += ds1*cf2;
dxdxi22 += ds2*cf2;
}
dxdxi[ip*sdxdxi+3*0+0] = dxdxi00;
dxdxi[ip*sdxdxi+3*0+1] = dxdxi01;
dxdxi[ip*sdxdxi+3*0+2] = dxdxi02;
dxdxi[ip*sdxdxi+3*1+0] = dxdxi10;
dxdxi[ip*sdxdxi+3*1+1] = dxdxi11;
dxdxi[ip*sdxdxi+3*1+2] = dxdxi12;
dxdxi[ip*sdxdxi+3*2+0] = dxdxi20;
dxdxi[ip*sdxdxi+3*2+1] = dxdxi21;
dxdxi[ip*sdxdxi+3*2+2] = dxdxi22;
*/
}
}
}
// NgProfiler::StopTimer (timer5);
// NgProfiler::StopTimer (timer);
}
template
void CurvedElements ::
CalcMultiPointElementTransformation
(ElementIndex elnr, int n,
const double * xi, size_t sxi,
double * x, size_t sx,
double * dxdxi, size_t sdxdxi);
template
void CurvedElements ::
CalcMultiPointElementTransformation
(ElementIndex elnr, int n,
const SIMD<double> * xi, size_t sxi,
SIMD<double> * x, size_t sx,
SIMD<double> * dxdxi, size_t sdxdxi);
};
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