oomph::SurfaceDerivatives Class Reference

#include <interface_elements.h>

Inheritance diagram for oomph::SurfaceDerivatives:

Public Member Functions
	SurfaceDerivatives ()

Protected Member Functions
double	compute_surface_derivatives (const Shape &psi, const DShape &dpsids, const DenseMatrix< double > &interpolated_t, const Vector< double > &interpolated_x, DShape &surface_gradient, DShape &surface_divergence)
	Fill in the specific surface derivative calculations. More...

Detailed Description

Class that establishes the surface derivative functions for SurfaceInterfaceElements (2D surfaces in 3D space) These are defined in a separate class so that they can be used by other interface equation-type classes.

Constructor & Destructor Documentation

SurfaceDerivatives()

oomph::SurfaceDerivatives::SurfaceDerivatives ( )

inline

{}

Member Function Documentation

compute_surface_derivatives()

double oomph::SurfaceDerivatives::compute_surface_derivatives ( const Shape &  psi, const DShape &  dpsids, const DenseMatrix< double > &  interpolated_t, const Vector< double > &  interpolated_x, DShape &  dpsidS, DShape &  dpsidS_div  )

protected

Fill in the specific surface derivative calculations.

Specialise the surface derivatives for 2D surface case.

///////////////////////////////////////////////////////////////////// ///////////////////////////////////////////////////////////////////// /////////////////////////////////////////////////////////////////////

  {
    const unsigned n_shape = psi.nindex1();
    const unsigned n_dim = 3;
 
    // Calculate the local metric tensor
    // The dot product of the two tangent vectors
    double amet[2][2];
    for (unsigned al = 0; al < 2; al++)
    {
      for (unsigned be = 0; be < 2; be++)
      {
        // Initialise to zero
        amet[al][be] = 0.0;
        // Add the dot product contributions
        for (unsigned i = 0; i < n_dim; i++)
        {
          amet[al][be] += interpolated_t(al, i) * interpolated_t(be, i);
        }
      }
    }
 
    // Work out the determinant
    double det_a = amet[0][0] * amet[1][1] - amet[0][1] * amet[1][0];
    // Also work out the contravariant metric
    double aup[2][2];
    aup[0][0] = amet[1][1] / det_a;
    aup[0][1] = -amet[0][1] / det_a;
    aup[1][0] = -amet[1][0] / det_a;
    aup[1][1] = amet[0][0] / det_a;
 
 
    // Now construct the surface gradient terms
    for (unsigned l = 0; l < n_shape; l++)
    {
      // Do some pre-computation
      const double dpsi_temp[2] = {
        aup[0][0] * dpsids(l, 0) + aup[0][1] * dpsids(l, 1),
        aup[1][0] * dpsids(l, 0) + aup[1][1] * dpsids(l, 1)};
 
      for (unsigned i = 0; i < n_dim; i++)
      {
        dpsidS(l, i) = dpsi_temp[0] * interpolated_t(0, i) +
                       dpsi_temp[1] * interpolated_t(1, i);
      }
    }
 
    // The divergence operator is the same
    dpsidS_div = dpsidS;
 
    // Return the jacobian
    return sqrt(det_a);
  }

References i, oomph::Shape::nindex1(), and sqrt().

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

• interface_elements.h
• interface_elements.cc