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LineEdgeBasis.cpp

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    HighOrder.cpp 60.03 KiB
    // Gmsh - Copyright (C) 1997-2019 C. Geuzaine, J.-F. Remacle
    //
    // See the LICENSE.txt file for license information. Please report all
    // issues on https://gitlab.onelab.info/gmsh/gmsh/issues.
    //
    // Contributor(s):
    //   Koen Hillewaert
    //
    
    #include <sstream>
    #include <vector>
    #include "GmshConfig.h"
    #include "HighOrder.h"
    #include "MLine.h"
    #include "MTriangle.h"
    #include "MQuadrangle.h"
    #include "MTetrahedron.h"
    #include "MHexahedron.h"
    #include "MPrism.h"
    #include "MPyramid.h"
    #include "GmshMessage.h"
    #include "OS.h"
    #include "fullMatrix.h"
    #include "BasisFactory.h"
    #include "InnerVertexPlacement.h"
    #include "Context.h"
    
    #if defined(HAVE_OPTHOM)
    #include "HighOrderMeshFastCurving.h"
    #include "HighOrderMeshPeriodicity.h"
    #endif
    
    // Functions that help optimizing placement of points on geometry
    
    // The aim here is to build a polynomial representation that consist
    // in polynomial segments of equal length
    
    static double mylength(GEdge *ge, int i, double *u)
    {
      return ge->length(u[i], u[i + 1], 10);
    }
    
    static void myresid(int N, GEdge *ge, double *u, fullVector<double> &r,
                        double *weight = NULL)
    {
      double L[100];
      for(int i = 0; i < N - 1; i++) L[i] = mylength(ge, i, u);
      if(weight)
        for(int i = 0; i < N - 2; i++)
          r(i) = L[i + 1] / weight[i + 1] - L[i] / weight[i];
      else
        for(int i = 0; i < N - 2; i++) r(i) = L[i + 1] - L[i];
    }
    
    static bool computeEquidistantParameters(GEdge *ge, double u0, double uN, int N,
                                             double *u, double underRelax)
    {
      const double PRECISION = 1.e-6;
      const int MAX_ITER = 50;
      const double eps = (uN - u0) * 1.e-5;
    
      // newton algorithm
      // N is the total number of points (3 for quadratic, 4 for cubic ...)
      // u[0] = u0;
      // u[N-1] = uN;
      // initialize as equidistant in parameter space
      u[0] = u0;
      double du = (uN - u0) / (N - 1);
      for(int i = 1; i < N; i++) {
        u[i] = u[i - 1] + du;