HierarchicalBasisHcurlTetra.h

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// Gmsh - Copyright (C) 1997-2022 C. Geuzaine, J.-F. Remacle
//
// See the LICENSE.txt file in the Gmsh root directory for license information.
// Please report all issues on https://gitlab.onelab.info/gmsh/gmsh/issues.
//
// Contributed by Ismail Badia.
 
// Reference :  "Higher-Order Finite Element  Methods"; Pavel Solin, Karel
// Segeth, Ivo Dolezel, Chapman and Hall/CRC; Edition : Har/Cdr (2003).
 
#ifndef HIERARCHICAL_BASIS_HCURL_TETRA_H
#define HIERARCHICAL_BASIS_HCURL_TETRA_H
 
#include <stdexcept>
#include <math.h>
#include "HierarchicalBasisHcurl.h"
 
/*
 * MTetrahedron
 *
 *                      v
 *                    .
 *                  ,/
 *                 /
 *              2
 *            ,/|`\
 *          ,/  |  `\
 *        ,/    '.   `\
 *      ,/       |     `\
 *    ,/         |       `\
 *   0-----------'.--------1 --> u
 *    `\.         |      ,/
 *       `\.      |    ,/
 *          `\.   '. ,/
 *             `\. |/
 *                `3
 *                   `\.
 *                      ` w
 *
 *
 *  Oriented Edges:
 * e0={0, 1}, e1={1, 2}, e2={2, 0}, e3={0, 3}, e4={2, 3}, e5={1, 3}
 *
 *
 * Oritented Surface:
 *  s0={0, 1, 2}, s1={0, 1, 3}, s2={0, 2, 3}, s3={1, 2, 3}
 * Local (directional) orders on mesh faces are not allowed to exceed the mini-
 * mum of the (appropriate directional) orders of approximation associated with
 * the interior of the adjacent elements. Local orders of approximation on mesh
 * edges are limited by the minimum of all (appropriate directional) orders cor-
 * responding to faces sharing that edge
 */
class HierarchicalBasisHcurlTetra : public HierarchicalBasisHcurl {
public:
  HierarchicalBasisHcurlTetra(int order);
  virtual ~HierarchicalBasisHcurlTetra();
  virtual unsigned int getNumberOfOrientations() const;
  virtual void generateBasis(double const &u, double const &v, double const &w,
                             std::vector<std::vector<double> > &vertexBasis,
                             std::vector<std::vector<double> > &edgeBasis,
                             std::vector<std::vector<double> > &faceBasis,
                             std::vector<std::vector<double> > &bubbleBasis,
                             std::string typeFunction)
  {
    if(typeFunction == "HcurlLegendre") {
      generateHcurlBasis(u, v, w, edgeBasis, faceBasis, bubbleBasis);
    }
    else if("CurlHcurlLegendre" == typeFunction) {
      generateCurlBasis(u, v, w, edgeBasis, faceBasis, bubbleBasis);
    }
    else {
      throw std::runtime_error("unknown typeFunction");
    }
  }
 
  virtual void
  orientEdge(int const &flagOrientation, int const &edgeNumber,
             std::vector<std::vector<double> > &edgeBasis,
             const std::vector<std::vector<double> > &eTablePositiveFlag,
             const std::vector<std::vector<double> > &eTableNegativeFlag);
  virtual void orientEdgeFunctionsForNegativeFlag(
    std::vector<std::vector<double> > &edgeFunctions);
  virtual void orientFace(
    int const &flag1, int const &flag2, int const &flag3, int const &faceNumber,
    const std::vector<std::vector<double> > &quadFaceFunctionsAllOrientation,
    const std::vector<std::vector<double> > &triFaceFunctionsAllOrientation,
    std::vector<std::vector<double> > &fTableCopy);
  virtual void getKeysInfo(std::vector<int> &functionTypeInfo,
                           std::vector<int> &orderInfo);
 
private:
  int _pb; // bubble function order
  int _pOrderEdge[6]; // Edge functions order (pOrderEdge[0] matches the order
                      // of the edge 0)
  int _pOrderFace[4]; // Face functions order in direction
  static double
  _affineCoordinate(const int &j, const double &u, const double &v,
                    const double &w); // affine coordinate lambdaj j=1..4
 
  virtual void
  generateHcurlBasis(double const &u, double const &v, double const &w,
                     std::vector<std::vector<double> > &edgeBasis,
                     std::vector<std::vector<double> > &faceBasis,
                     std::vector<std::vector<double> > &bubbleBasis);
 
  virtual void
  generateCurlBasis(double const &u, double const &v, double const &w,
                    std::vector<std::vector<double> > &edgeBasis,
                    std::vector<std::vector<double> > &faceBasis,
                    std::vector<std::vector<double> > &bubbleBasis);
 
  static double dotProduct(const std::vector<double> &u,
                           const std::vector<double> &v);
  inline void gradient(const double &lambda1, const double &lambda2,
                       const std::vector<double> &dlambda1,
                       const std::vector<double> &dlambda2,
                       std::vector<double> &result); // grad(u)v+grad(v)u
  inline void curlFunction(const double &a, const std::vector<double> &nD,
                           const std::vector<double> &grad,
                           std::vector<double> &result);
  virtual void orientOneFace(double const &u, double const &v, double const &w,
                             int const &flag1, int const &flag2,
                             int const &flag3, int const &faceNumber,
                             std::vector<std::vector<double> > &faceFunctions,
                             std::string typeFunction);
};
 
#endif