netgen/libsrc/meshing/fieldlines.cpp

#include <mystdlib.h>

#include <myadt.hpp>
#include <meshing.hpp>
#include <csg.hpp>
#include <stlgeom.hpp>

#include "fieldlines.hpp"

namespace netgen
{
  RKStepper :: ~RKStepper() 
  {
    delete a;
  }
    
  RKStepper :: RKStepper(int type) : a(NULL), tolerance(1e100)
  {
    notrestarted = 0;

    if (type == 0) // explicit Euler
      {
	c.SetSize(1); c[0] = 0;
	b.SetSize(1); b[0] = 1;
	steps = order = 1;
      }
    else if (type == 1) // Euler-Cauchy
      {
	c.SetSize(2); c[0] = 0; c[1] = 0.5;
	b.SetSize(2); b[0] = 0; b[1] = 1;
	NgArray<int> size(2);
	size[0] = 0; size[1] = 1;
	a = new TABLE<double>(size);
	a->Set(2,1,0.5);  // Set, Get: 1-based!
	steps = order = 2;
      }
    else if (type == 2) // Simpson
      {
	c.SetSize(3); c[0] = 0; c[1] = 1; c[2] = 0.5;
	b.SetSize(3); b[0] = b[1] = 1./6.; b[2] = 2./3.;
	NgArray<int> size(3);
	size[0] = 0; size[1] = 1; size[2] = 2;
	a = new TABLE<double>(size);
	a->Set(2,1,1);
	a->Set(3,1,0.25); a->Set(3,2,0.25); 
	steps = order = 3;
      }
    else if (type == 3) // classical Runge-Kutta
      {
	c.SetSize(4); c[0] = 0; c[1] = c[2] = 0.5; c[3] = 1;
	b.SetSize(4); b[0] = b[3] = 1./6.; b[1] = b[2] = 1./3.;
	NgArray<int> size(4);
	size[0] = 0; size[1] = 1; size[2] = 2; size[3] = 3;
	a = new TABLE<double>(size);
	a->Set(2,1,0.5);
	a->Set(3,1,0); a->Set(3,2,0.5); 
	a->Set(4,1,0); a->Set(4,2,0); a->Set(4,3,1); 
	steps = order = 4;
      }
    
    K.SetSize(steps);
  }

  void RKStepper :: StartNextValCalc(const Point<3> & astartval, const double astartt, const double ah, const bool aadaptive)
  {
    //cout << "Starting RK-Step with h=" << ah << endl;

    stepcount = 0;
    h = ah;
    startt = astartt;
    startval = astartval;
    adaptive = aadaptive;
    adrun = 0;
  }

  bool RKStepper :: GetNextData(Point<3> & val, double & t, double & ah)
  {
    bool finished = false;
    
    if(stepcount <= steps && stepcount>0)
      {
	t = startt + c[stepcount-1]*h;
	val = startval;
	for(int i=0; i<stepcount-1; i++)
	  val += h * a->Get(stepcount,i+1) * K[i];
      }
    
    
    if(stepcount == steps)
      {
	val = startval;
	for(int i=0; i<steps; i++)
	  val += h * b[i] * K[i];
	
	if(adaptive)
	  {
	    if(adrun == 0)
	      {
		stepcount = 0;
		h *= 0.5;
		adrun = 1;
		valh = val;
	      }
	    else if (adrun == 1)
	      {
		stepcount = 0;
		startval_bak = startval;
		startval = val;
		startt_bak = startt;
		startt += h;//0.5*h;
		adrun = 2;
	      }
	    else if (adrun == 2)
	      {
		Point<3> valh2 = val;
		val = valh2 + 1./(pow(2.,order)-1.) * (valh2 - valh);
		auto errvec = val - valh;
		
		double err = errvec.Length();
		
		double fac = 0.7 * pow(tolerance/err,1./(order+1.));
		if(fac > 1.3) fac = 1.3;
		
		if(fac < 1 || notrestarted >= 2)
		  ah = 2.*h * fac;
		
		if(err < tolerance) 
		  {
		    finished = true;
		    notrestarted++;
		    //(*testout) << "finished RK-Step, new h=" << ah << " tolerance " << tolerance << " err " << err << endl;
		  }
		else
		  {
		    //ah *= 0.9;
		    notrestarted = 0;
		    //(*testout) << "restarting h " << 2.*h << " ah " << ah << " tolerance " << tolerance << " err " << err << endl;
		    StartNextValCalc(startval_bak,startt_bak, ah, adaptive);
		  }
	      }
	  }
	else 
	  {
	    t = startt + h;
	    finished = true;
	  }
	
      }
    
    if(stepcount == 0)
      {
	t = startt + c[stepcount]*h;
	val = startval;
	for(int i=0; i<stepcount; i++)
	  val += h * a->Get(stepcount,i) * K[i];
      }
    
    return finished;
  }


  bool RKStepper :: FeedNextF(const Vec<3> & f)
  {
    K[stepcount] = f;
    stepcount++;
    return true;
  }
  


  void FieldLineCalc :: GenerateFieldLines(Array<Point<3>> & potential_startpoints, const int numlines)
  {

    
    Array<Point<3>> line_points;
    Array<double> line_values;
    Array<bool> drawelems;
    Array<int> dirstart;
    pstart.SetSize0();
    pend.SetSize0();
    values.SetSize0();

    double crit = 1.0;

    if(randomized)
      {
	double sum = 0;
	double lami[3];
        Vec<3> v;
	
	for(int i=0; i<potential_startpoints.Size(); i++)
	  {
	    int elnr = mesh.GetElementOfPoint(potential_startpoints[i],lami,true) - 1;
	    if(elnr == -1)
	      continue;

	    mesh.SetPointSearchStartElement(elnr);
	    
            func(elnr, lami, v);
            sum += v.Length();
	  }

	crit = sum/double(numlines);
      }


    int calculated = 0;

    for(int i=0; i<potential_startpoints.Size(); i++)
      {
	if(randomized)
	  SetCriticalValue((double(rand())/RAND_MAX)*crit);

	if(calculated >= numlines) break;

	Calc(potential_startpoints[i],line_points,line_values,drawelems,dirstart);

	bool usable = false;

	for(int j=1; j<dirstart.Size(); j++)
	  for(int k=dirstart[j-1]; k<dirstart[j]-1; k++)
	    {
	      if(!drawelems[k] || !drawelems[k+1]) continue;
	     
	      usable = true;
              pstart.Append(line_points[k]);
              pend.Append(line_points[k+1]);
              values.Append( 0.5*(line_values[k]+line_values[k+1]) );
	    }

	if(usable) calculated++;
      }
    
  }



  FieldLineCalc :: FieldLineCalc(const Mesh & amesh, const VectorFunction & afunc,
				 const double rel_length, const int amaxpoints, 
				 const double rel_thickness, const double rel_tolerance, const int rk_type, const int adirection) :
    mesh(amesh), func(afunc), stepper(rk_type)
  {
    mesh.GetBox (pmin, pmax);
    rad = 0.5 * Dist (pmin, pmax);
    

    maxlength = (rel_length > 0) ? rel_length : 0.5;
    maxlength *= 2.*rad;

    thickness = (rel_thickness > 0) ? rel_thickness : 0.0015;
    thickness *= 2.*rad;
    
    double auxtolerance = (rel_tolerance > 0) ? rel_tolerance : 1.5e-3;
    auxtolerance *= 2.*rad;

    stepper.SetTolerance(auxtolerance);
    
    direction = adirection;
    
    
    maxpoints = amaxpoints;

    if(direction == 0)
      {
	maxlength *= 0.5;
	maxpoints /= 2;
      }
    

    critical_value = -1;

    randomized = false;
    
  }
  

  FieldLineCalc :: ~FieldLineCalc() {;}

  
  void FieldLineCalc :: Calc(const Point<3> & startpoint, Array<Point<3>> & points, Array<double> & vals, Array<bool> & drawelems, Array<int> & dirstart)
  {
    Vec<3> v = 0.0;
    double startlami[3] = {0.0, 0.0, 0.0};
    
    points.SetSize(0);
    vals.SetSize(0);
    drawelems.SetSize(0);

    dirstart.SetSize(0);
    dirstart.Append(0);


    int startelnr = mesh.GetElementOfPoint(startpoint,startlami,true) - 1;
    (*testout) << "p = " << startpoint << "; elnr = " << startelnr << endl;
    if (startelnr == -1)
      return;
      
    mesh.SetPointSearchStartElement(startelnr);

    Vec<3> startv;
    bool startdraw = func(startelnr, startlami, startv);

    double startval = startv.Length();

    if(critical_value > 0 && fabs(startval) < critical_value)
      return;

    //cout << "p = " << startpoint << "; elnr = " << startelnr << endl;


      
    for(int dir = 1; dir >= -1; dir -= 2)
      {
	if(dir*direction < 0) continue;
	  
	points.Append(startpoint);
	vals.Append(startval);
	drawelems.Append(startdraw);
	  
	double h = 0.001*rad/startval; // otherwise no nice lines; should be made accessible from outside
	
	v = startv;
	if(dir == -1) v *= -1.;

	int elnr = startelnr;
        double lami[3] = { startlami[0], startlami[1], startlami[2]}; 
	  

	for(double length = 0; length < maxlength; length += h*vals.Last())
	  {
	    if(v.Length() < 1e-12*rad)
	      {
		(*testout) << "Current fieldlinecalculation came to a stillstand at " << points.Last() << endl;
		break;
	      }

            double dummyt{0};
	    stepper.StartNextValCalc(points.Last(),dummyt,h,true);
	    stepper.FeedNextF(v);
            bool drawelem = false;

            Point<3> newp;
	    while(!stepper.GetNextData(newp,dummyt,h) && elnr != -1)
	      {
		elnr = mesh.GetElementOfPoint(newp,lami,true) - 1;
		if(elnr != -1)
		  {
		    mesh.SetPointSearchStartElement(elnr);
                    drawelem = func(elnr, lami, v);
		    if(dir == -1) v *= -1.;
		    stepper.FeedNextF(v);
		  }
	      }

	    if (elnr == -1)
	      {
		//cout << "direction " <<dir << " reached the wall." << endl;
		break;
	      }

	    points.Append(newp);
	    vals.Append(v.Length());
	    drawelems.Append(drawelem);

	    if(points.Size() % 40 == 0 && points.Size() > 1)
	      (*testout) << "Points in current fieldline: " << points.Size() << ", current position: " << newp << endl;

	    if(maxpoints > 0 && points.Size() >= maxpoints)
	      {
		break;
	      }

	    //cout << "length " << length << " h " << h << " vals.Last() " << vals.Last()  << " maxlength " << maxlength << endl;
	  }
	dirstart.Append(points.Size());
      }
  }
  
}