oomph::TElementShape< 2, 3 > Class Reference

#include <Telements.h>

Public Member Functions
void	local_coordinate_of_node (const unsigned &j, Vector< double > &s) const
	Return local coordinates of node j. More...
void	shape (const Vector< double > &s, Shape &psi) const
	Shape function for specific TElement<2,3> More...
void	dshape_local (const Vector< double > &s, Shape &psi, DShape &dpsids) const
	Derivatives of shape functions for specific TElement<2,3> More...
void	d2shape_local (const Vector< double > &s, Shape &psi, DShape &dpsids, DShape &d2psids) const

Member Function Documentation

d2shape_local()

void oomph::TElementShape< 2, 3 >::d2shape_local ( const Vector< double > &  s, Shape &  psi, DShape &  dpsids, DShape &  d2psids  ) const

inline

Second derivatives of shape functions for specific TElement<2,3>: d2psids(i,0) = \( \partial^2 \psi_j / \partial s_0^2 \) d2psids(i,1) = \( \partial^2 \psi_j / \partial s_1^2 \) d2psids(i,2) = \( \partial^2 \psi_j / \partial s_0 \partial s_1 \)

    {
      // ALH: Don't know why object qualifier is needed
      this->dshape_local(s, psi, dpsids);
 
      d2psids(0, 0) = 4.0;
      d2psids(0, 1) = 0.0;
      d2psids(0, 2) = 0.0;
 
      d2psids(1, 0) = 0.0;
      d2psids(1, 1) = 4.0;
      d2psids(1, 2) = 0.0;
 
      d2psids(2, 0) = 4.0;
      d2psids(2, 1) = 4.0;
      d2psids(2, 2) = 4.0;
 
      d2psids(3, 0) = 0.0;
      d2psids(3, 1) = 0.0;
      d2psids(3, 2) = 4.0;
 
      d2psids(4, 0) = 0.0;
      d2psids(4, 1) = -8.0;
      d2psids(4, 2) = -4.0;
 
      d2psids(5, 0) = -8.0;
      d2psids(5, 1) = 0.0;
      d2psids(5, 2) = -4.0;
    }

References s.

dshape_local()

void oomph::TElementShape< 2, 3 >::dshape_local ( const Vector< double > &  s, Shape &  psi, DShape &  dpsids  ) const

inline

Derivatives of shape functions for specific TElement<2,3>

    {
      // ALH: Don't know why object qualifier is needed
      this->shape(s, psi);
 
      dpsids(0, 0) = 4.0 * s[0] - 1.0;
      dpsids(0, 1) = 0.0;
      dpsids(1, 0) = 0.0;
      dpsids(1, 1) = 4.0 * s[1] - 1.0;
      dpsids(2, 0) = 2.0 * (2.0 * s[0] - 1.5 + 2.0 * s[1]);
      dpsids(2, 1) = 2.0 * (2.0 * s[0] - 1.5 + 2.0 * s[1]);
      dpsids(3, 0) = 4.0 * s[1];
      dpsids(3, 1) = 4.0 * s[0];
      dpsids(4, 0) = -4.0 * s[1];
      dpsids(4, 1) = 4.0 * (1.0 - s[0] - 2.0 * s[1]);
      dpsids(5, 0) = 4.0 * (1.0 - 2.0 * s[0] - s[1]);
      dpsids(5, 1) = -4.0 * s[0];
    }

References s, and oomph::OneDimLagrange::shape().

local_coordinate_of_node()

void oomph::TElementShape< 2, 3 >::local_coordinate_of_node ( const unsigned &  j, Vector< double > &  s  ) const

inline

Return local coordinates of node j.

    {
      s.resize(2);
 
      switch (j)
      {
        case 0:
          s[0] = 1.0;
          s[1] = 0.0;
          break;
 
        case 1:
          s[0] = 0.0;
          s[1] = 1.0;
          break;
 
        case 2:
          s[0] = 0.0;
          s[1] = 0.0;
          break;
 
        case 3:
          s[0] = 0.5;
          s[1] = 0.5;
          break;
 
        case 4:
          s[0] = 0.0;
          s[1] = 0.5;
          break;
 
        case 5:
          s[0] = 0.5;
          s[1] = 0.0;
          break;
 
        default:
          std::ostringstream error_message;
          error_message
            << "Element only has six nodes; called with node number " << j
            << std::endl;
 
          throw OomphLibError(error_message.str(),
                              OOMPH_CURRENT_FUNCTION,
                              OOMPH_EXCEPTION_LOCATION);
      }
    }

References j, OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION, and s.

shape()

void oomph::TElementShape< 2, 3 >::shape ( const Vector< double > &  s, Shape &  psi  ) const

inline

Shape function for specific TElement<2,3>

    {
      // Reconstruct the third area coordinate
      double s_2 = 1.0 - s[0] - s[1];
 
      // note that s[2] needs replacing by s_2 everywhere since only
      // two independent variables s[0],s[1] and s_2 is expressed in terms of
      // those later.
      psi[0] = 2.0 * s[0] * (s[0] - 0.5);
      psi[1] = 2.0 * s[1] * (s[1] - 0.5);
      psi[2] = 2.0 * s_2 * (s_2 - 0.5);
      psi[3] = 4.0 * s[0] * s[1];
      psi[4] = 4.0 * s[1] * s_2;
      psi[5] = 4.0 * s_2 * s[0];
    }

References s.

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The documentation for this class was generated from the following file:

• Telements.h