MixedExactSolution Class Reference

#include <mixed_exact_solution.h>

Public Member Functions
	MixedExactSolution ()=default
	~MixedExactSolution ()=default
Real	scalar (Real x, Real y)
Real	scalar (Real x, Real y, Real z)
RealGradient	operator() (Real x, Real y)
RealGradient	operator() (Real x, Real y, Real z)
RealTensor	grad (Real x, Real y)
RealTensor	grad (Real x, Real y, Real z)
Real	div (Real x, Real y)
Real	div (Real x, Real y, Real z)
Real	forcing (Real x, Real y)
Real	forcing (Real x, Real y, Real z)

Detailed Description

Definition at line 26 of file mixed_exact_solution.h.

Constructor & Destructor Documentation

MixedExactSolution()

MixedExactSolution::MixedExactSolution ( )

default

~MixedExactSolution()

MixedExactSolution::~MixedExactSolution ( )

default

Member Function Documentation

div() [1/2]

Real MixedExactSolution::div ( Real  x, Real  y  )

inline

Definition at line 84 of file mixed_exact_solution.h.

  {
    const Real dux_dx = grad(x, y)(0, 0);
    const Real duy_dy = grad(x, y)(1, 1);
 
    return dux_dx + duy_dy;
  }

References grad(), and libMesh::Real.

Referenced by forcing(), and forcing().

div() [2/2]

Real MixedExactSolution::div ( Real  x, Real  y, Real  z  )

inline

Definition at line 92 of file mixed_exact_solution.h.

  {
    const Real dux_dx = grad(x, y, z)(0, 0);
    const Real duy_dy = grad(x, y, z)(1, 1);
    const Real duz_dz = grad(x, y, z)(2, 2);
 
    return dux_dx + duy_dy + duz_dz;
  }

References grad(), and libMesh::Real.

forcing() [1/2]

Real MixedExactSolution::forcing ( Real  x, Real  y  )

inline

Definition at line 101 of file mixed_exact_solution.h.

  {
    return div(x, y);
  }

References div().

Referenced by alternative_fe_assembly(), compute_enriched_soln(), and fe_assembly().

forcing() [2/2]

Real MixedExactSolution::forcing ( Real  x, Real  y, Real  z  )

inline

Definition at line 106 of file mixed_exact_solution.h.

  {
    return div(x, y, z);
  }

References div().

grad() [1/2]

RealTensor MixedExactSolution::grad ( Real  x, Real  y  )

inline

Definition at line 59 of file mixed_exact_solution.h.

  {
    const Real dux_dx = .5*pi*.5*pi*cos(.5*pi*x)*sin(.5*pi*y);
    const Real dux_dy = .5*pi*.5*pi*sin(.5*pi*x)*cos(.5*pi*y);
    const Real duy_dx = .5*pi*.5*pi*sin(.5*pi*x)*cos(.5*pi*y);
    const Real duy_dy = .5*pi*.5*pi*cos(.5*pi*x)*sin(.5*pi*y);
 
    return RealTensor(dux_dx, dux_dy, Real(0), duy_dx, duy_dy);
  }

References libMesh::pi, and libMesh::Real.

Referenced by div(), and div().

grad() [2/2]

RealTensor MixedExactSolution::grad ( Real  x, Real  y, Real  z  )

inline

Definition at line 69 of file mixed_exact_solution.h.

  {
    const Real dux_dx =  .5*pi*.5*pi*cos(.5*pi*x)*sin(.5*pi*y)*cos(.5*pi*z);
    const Real dux_dy =  .5*pi*.5*pi*sin(.5*pi*x)*cos(.5*pi*y)*cos(.5*pi*z);
    const Real dux_dz = -.5*pi*.5*pi*sin(.5*pi*x)*sin(.5*pi*y)*sin(.5*pi*z);
    const Real duy_dx =  .5*pi*.5*pi*sin(.5*pi*x)*cos(.5*pi*y)*cos(.5*pi*z);
    const Real duy_dy =  .5*pi*.5*pi*cos(.5*pi*x)*sin(.5*pi*y)*cos(.5*pi*z);
    const Real duy_dz =  .5*pi*.5*pi*cos(.5*pi*x)*cos(.5*pi*y)*sin(.5*pi*z);
    const Real duz_dx = -.5*pi*.5*pi*sin(.5*pi*x)*sin(.5*pi*y)*sin(.5*pi*z);
    const Real duz_dy =  .5*pi*.5*pi*cos(.5*pi*x)*cos(.5*pi*y)*sin(.5*pi*z);
    const Real duz_dz =  .5*pi*.5*pi*cos(.5*pi*x)*sin(.5*pi*y)*cos(.5*pi*z);
 
    return RealTensor(dux_dx, dux_dy, dux_dz, duy_dx, duy_dy, duy_dz, duz_dx, duz_dy, duz_dz);
  }

References libMesh::pi, and libMesh::Real.

operator()() [1/2]

RealGradient MixedExactSolution::operator() ( Real  x, Real  y  )

inline

Definition at line 42 of file mixed_exact_solution.h.

  {
    const Real ux =  .5*pi*sin(.5*pi*x)*sin(.5*pi*y);
    const Real uy = -.5*pi*cos(.5*pi*x)*cos(.5*pi*y);
 
    return RealGradient(ux, uy);
  }

References libMesh::pi, and libMesh::Real.

operator()() [2/2]

RealGradient MixedExactSolution::operator() ( Real  x, Real  y, Real  z  )

inline

Definition at line 50 of file mixed_exact_solution.h.

  {
    const Real ux =  .5*pi*sin(.5*pi*x)*sin(.5*pi*y)*cos(.5*pi*z);
    const Real uy = -.5*pi*cos(.5*pi*x)*cos(.5*pi*y)*cos(.5*pi*z);
    const Real uz =  .5*pi*cos(.5*pi*x)*sin(.5*pi*y)*sin(.5*pi*z);
 
    return RealGradient(ux, uy, uz);
  }

References libMesh::pi, and libMesh::Real.

scalar() [1/2]

Real MixedExactSolution::scalar ( Real  x, Real  y  )

inline

Definition at line 32 of file mixed_exact_solution.h.

  {
    return cos(.5*pi*x)*sin(.5*pi*y);
  }

References libMesh::pi.

Referenced by alternative_fe_assembly(), and fe_assembly().

scalar() [2/2]

Real MixedExactSolution::scalar ( Real  x, Real  y, Real  z  )

inline

Definition at line 37 of file mixed_exact_solution.h.

  {
    return cos(.5*pi*x)*sin(.5*pi*y)*cos(.5*pi*z);
  }

References libMesh::pi.

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

• examples/vector_fe/vector_fe_ex8/mixed_exact_solution.h