CurlCurlExactSolution Class Reference

#include <curl_curl_exact_solution.h>

Public Member Functions
	CurlCurlExactSolution ()
	~CurlCurlExactSolution ()
RealGradient	operator() (Real x, Real y)
RealTensor	grad (Real x, Real y)
RealGradient	curl (Real x, Real y)
RealGradient	forcing (Real x, Real y)
	CurlCurlExactSolution ()
	~CurlCurlExactSolution ()
RealGradient	operator() (Real x, Real y, Real z)
RealTensor	grad (Real x, Real y, Real z)
RealGradient	curl (Real x, Real y, Real z)
RealGradient	forcing (Real x, Real y, Real z)

Detailed Description

Definition at line 26 of file curl_curl_exact_solution.h.

Constructor & Destructor Documentation

CurlCurlExactSolution() [1/2]

CurlCurlExactSolution::CurlCurlExactSolution ( )

inline

Definition at line 29 of file curl_curl_exact_solution.h.

{}

~CurlCurlExactSolution() [1/2]

CurlCurlExactSolution::~CurlCurlExactSolution ( )

inline

Definition at line 31 of file curl_curl_exact_solution.h.

{}

CurlCurlExactSolution() [2/2]

CurlCurlExactSolution::CurlCurlExactSolution ( )

inline

Definition at line 29 of file curl_curl_exact_solution.h.

{}

~CurlCurlExactSolution() [2/2]

CurlCurlExactSolution::~CurlCurlExactSolution ( )

inline

Definition at line 31 of file curl_curl_exact_solution.h.

{}

Member Function Documentation

curl() [1/2]

RealGradient CurlCurlExactSolution::curl ( Real  x, Real  y  )

inline

Definition at line 51 of file curl_curl_exact_solution.h.

  {
    const Real dux_dy =  pi*cos(pi*x)*cos(pi*y);
    const Real duy_dx = -pi*cos(pi*x)*cos(pi*y);
 
    return RealGradient(Real(0), Real(0), duy_dx - dux_dy);
  }

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

curl() [2/2]

RealGradient CurlCurlExactSolution::curl ( Real  x, Real  y, Real  z  )

inline

Definition at line 59 of file curl_curl_exact_solution.h.

  {
    const Real duz_dy = (1.0 - x*x)*(-2.0*y);
    const Real duy_dz = (1.0 - x*x)*(-2.0*z);
 
    const Real dux_dz = (1.0 - y*y)*(-2.0*z);
    const Real duz_dx = (1.0 - y*y)*(-2.0*x);
 
    const Real dux_dy = (1.0 - z*z)*(-2.0*y);
    const Real duy_dx = (1.0 - z*z)*(-2.0*x);
 
    return RealGradient(duz_dy - duy_dz, dux_dz - duz_dx, duy_dx - dux_dy);
  }

References libMesh::Real.

forcing() [1/2]

RealGradient CurlCurlExactSolution::forcing ( Real  x, Real  y  )

inline

Definition at line 59 of file curl_curl_exact_solution.h.

  {
    const Real fx =  (2*pi*pi + 1)*cos(pi*x)*sin(pi*y);
    const Real fy = -(2*pi*pi + 1)*sin(pi*x)*cos(pi*y);
 
    return RealGradient(fx, fy);
  }

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

Referenced by CurlCurlSystem::forcing().

forcing() [2/2]

RealGradient CurlCurlExactSolution::forcing ( Real  x, Real  y, Real  z  )

inline

Definition at line 73 of file curl_curl_exact_solution.h.

  {
    const Real fx = 2.0*(1.0 - y*y) + 2.0*(1.0 - z*z) + (1.0 - y*y)*(1.0 - z*z);
    const Real fy = 2.0*(1.0 - x*x) + 2.0*(1.0 - z*z) + (1.0 - x*x)*(1.0 - z*z);
    const Real fz = 2.0*(1.0 - x*x) + 2.0*(1.0 - y*y) + (1.0 - x*x)*(1.0 - y*y);
 
    return RealGradient(fx, fy, fz);
  }

References libMesh::Real.

grad() [1/2]

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

inline

Definition at line 41 of file curl_curl_exact_solution.h.

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

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

grad() [2/2]

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

inline

Definition at line 42 of file curl_curl_exact_solution.h.

  {
    const Real dux_dx = 0.0;
    const Real dux_dy = (1.0 - z*z)*(-2.0*y);
    const Real dux_dz = (1.0 - y*y)*(-2.0*z);
 
    const Real duy_dx = (1.0 - z*z)*(-2.0*x);
    const Real duy_dy = 0.0;
    const Real duy_dz = (1.0 - x*x)*(-2.0*z);
 
    const Real duz_dx = (1.0 - y*y)*(-2.0*x);
    const Real duz_dy = (1.0 - x*x)*(-2.0*y);
    const Real duz_dz = 0.0;
 
    return RealTensor(dux_dx, dux_dy, dux_dz, duy_dx, duy_dy, duy_dz, duz_dx, duz_dy, duz_dz);
  }

References libMesh::Real.

operator()() [1/2]

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

inline

Definition at line 33 of file curl_curl_exact_solution.h.

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

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

operator()() [2/2]

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

inline

Definition at line 33 of file curl_curl_exact_solution.h.

  {
    const Real ux = (1.0 - y*y)*(1.0 - z*z);
    const Real uy = (1.0 - x*x)*(1.0 - z*z);
    const Real uz = (1.0 - x*x)*(1.0 - y*y);
 
    return RealGradient(ux, uy, uz);
  }

References libMesh::Real.

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

• examples/vector_fe/vector_fe_ex3/curl_curl_exact_solution.h