gmQuadShape.h

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/************************************************************************
**
** Copyright (C) 2014 by Carlos Augusto Teixera Mendes
** All rights reserved.
**
** This file is part of the "GeMA" software. It's use should respect
** the terms in the license agreement that can be found together 
** with this source code.
** It is provided AS IS, with NO WARRANTY OF ANY KIND, 
** INCLUDING THE WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR 
** A PARTICULAR PURPOSE.
**
************************************************************************/

#ifndef _GEMA_QUAD_SHAPE_H_
#define _GEMA_QUAD_SHAPE_H_

#include "gmShape.h"

//--------------------------------------------------------------------------------------------------------------------------
//      Quad Elements
//--------------------------------------------------------------------------------------------------------------------------

class GMC_API_EXPORT GmQuadShape: public GmShape
{
public:
  // See comments on the base class
  virtual int numNaturalCoord() const { return 2; }

  // See comments on the base class
  virtual int numCartesianCoord() const { return 2; }

  // See comments on the base class
  virtual void naturalCoordLimits(int coord, double* min, double* max) const { Q_UNUSED(coord); *min = -1.0; *max = 1.0; }

  // See comments on the base class
  virtual void naturalCenter(GmVector& coord) const { coord.zeros(2); } // Center = (0.0, 0.0) for all quads

  virtual bool translateEdgePoint(int edge, const GmVector& srcEdgeCoord, GmVector& elementCoord) const;

  // See comments on the base class. Undefined for surface elements.
  virtual bool translateFacePoint(int face, const GmVector& srcFaceCoord, GmVector& elementCoord) const
  {
    Q_UNUSED(face); Q_UNUSED(srcFaceCoord); Q_UNUSED(elementCoord); return false;
  }

  virtual double shapeCartesianPartialsFromPJ(const GmMatrix& P, const GmMatrix& J, GmMatrix& dN, bool transposed = false) const;

  // See comments on the base class
  virtual double scaledJacobianDet(const GmMatrix& J) const { return arma::det(J); }

  // See comments on the base class
  virtual void jacobianAndPartials(const GmVector& ncoord, const GmMatrix& X, GmMatrix& J, GmMatrix& P, bool transposed = false) const
  {
    jacIndependentNatCoord(ncoord, X, J, P, transposed);
  }

  // See comments on the base class
  virtual double borderScalingFactor(int border, const GmVector& borderCoord, const GmVector& elementCoord,
                                     const GmMatrix& X, bool transposed = false) const
  {
    return edgeScalingFactor(border, borderCoord, elementCoord, X, transposed);
  }

  virtual double edgeScalingFactor(int border, const GmVector& borderCoord, const GmVector& elementCoord,
                                   const GmMatrix& X, bool transposed = false) const;

  // See comments on the base class. Undefined for 2D elements.
  virtual double faceScalingFactor(int border, const GmVector& borderCoord, const GmVector& elementCoord,
                                   const GmMatrix& X, bool transposed = false) const
  {
    Q_UNUSED(border); Q_UNUSED(borderCoord); Q_UNUSED(elementCoord); Q_UNUSED(X); Q_UNUSED(transposed);
    return 0.0;
  }

  // fixedEdgeCoord() & Value() are made static since they are "reused" by Int3DQFace shape functions
  static int    fixedEdgeCoord(int border);
  static double fixedEdgeValue(int border);

protected:

  // See comments on the base class. Calls the default algorithm for Quad / Hex elements
  virtual bool gradientBasedCartesianToNatural(const GmVector& coord, const GmMatrix& X, double tol,
                                               int maxIter, double natTol, GmVector& ncoord, bool* inside) const
  {
    return gradientBasedCartesianToNaturalQuadHex(coord, X, tol, maxIter, natTol, ncoord, inside);
  }
};


class GMC_API_EXPORT GmQuad4Shape: public GmQuadShape
{
public:
  // See comments on the base class
  virtual GmCellType elemType() const { return GM_QUAD4; }

  // See comments on the base class
  virtual int numFunctions() const { return 4; }

  virtual void nodeNaturalCoord(int node, GmVector& coord) const;

  virtual void shapeValues  (const GmVector& ncoord, GmVector& N) const;
  virtual void shapePartials(const GmVector& ncoord, GmMatrix& dN, bool transposed = false) const;

protected:
  // See comments on the base class
  virtual bool hasGeometryBasedCartesianToNatural() const { return true; }

  virtual bool geometryBasedCartesianToNatural(const GmVector& coord, const GmMatrix& X, double natTol,
                                               GmVector& ncoord, bool* inside) const;
};

class GMC_API_EXPORT GmQuad8Shape : public GmQuadShape
{
public:
  // See comments on the base class
  virtual GmCellType elemType() const { return GM_QUAD8; }

  // See comments on the base class
  virtual int numFunctions() const { return 8; }

  virtual void nodeNaturalCoord(int node, GmVector& coord) const;

  // We previously had (by Erwan) a tentative implementation of a geometric method
  // for cartesian to natural based on the paper "Distorsion measures ans inverse mapping 
  // for isoparametric 8-node plane finite elements with curved boundaries" - Lautersztajn (1998) 
  // but it didn't worked and was removed

  virtual void shapeValues(const GmVector& ncoord, GmVector& N) const;
  virtual void shapePartials(const GmVector& ncoord, GmMatrix& dN, bool transposed = false) const;
};

class GMC_API_EXPORT GmQuad9Shape: public GmQuadShape
{
public:
  // See comments on the base class
  virtual GmCellType elemType() const { return GM_QUAD9; }

  // See comments on the base class
  virtual int numFunctions() const { return 9; }

  virtual void nodeNaturalCoord(int node, GmVector& coord) const;

  virtual void shapeValues  (const GmVector& ncoord, GmVector& N) const;
  virtual void shapePartials(const GmVector& ncoord, GmMatrix& dN, bool transposed = false) const;
};

class GMC_API_EXPORT GmQuad3D4Shape : public GmQuad4Shape
{
public:
  // See comments on the base class
  virtual GmCellType elemType() const { return GM_QUAD3D4; }
  virtual int numCartesianCoord() const { return 3; }

  // See comments on the base class
  virtual void jacIndependentNatCoord(const GmVector& ncoord, const GmMatrix& X, GmMatrix& J, GmMatrix& P, bool transposed) const;

protected:
  // Implementation of the geometric cartesian to natural method for Quad4 only works with 2D coordinates
  virtual bool hasGeometryBasedCartesianToNatural() const { return false; }

  // See comments on the base class. At the moment we don't have a working version for 3D quads
  virtual bool gradientBasedCartesianToNatural(const GmVector& coord, const GmMatrix& X, double tol,
                                               int maxIter, double natTol, GmVector& ncoord, bool* inside) const
  {
    Q_UNUSED(coord); Q_UNUSED(X); Q_UNUSED(tol); Q_UNUSED(maxIter); Q_UNUSED(natTol); Q_UNUSED(ncoord); Q_UNUSED(inside);
    return false;
  }

};

class GMC_API_EXPORT GmQuad3D8Shape : public GmQuad8Shape
{
public:
  // See comments on the base class
  virtual GmCellType elemType() const { return GM_QUAD3D8; }
  virtual int numCartesianCoord() const { return 3; }

  virtual void jacIndependentNatCoord(const GmVector& ncoord, const GmMatrix& X, GmMatrix& J, GmMatrix& P, bool transposed) const;

protected:
  // See comments on the base class. At the moment we don't have a working version for 3D quads
  virtual bool gradientBasedCartesianToNatural(const GmVector& coord, const GmMatrix& X, double tol,
                                               int maxIter, double natTol, GmVector& ncoord, bool* inside) const
  {
    Q_UNUSED(coord); Q_UNUSED(X); Q_UNUSED(tol); Q_UNUSED(maxIter); Q_UNUSED(natTol); Q_UNUSED(ncoord); Q_UNUSED(inside);
    return false;
  }
};


#endif