CurlCurlExactSolution Class Reference

#include <curl_curl_exact_solution.h>

Public Member Functions
	CurlCurlExactSolution ()=default
	~CurlCurlExactSolution ()=default
RealGradient	operator() (Point p)
RealTensor	grad (Point p)
RealGradient	forcing (Point p)
	CurlCurlExactSolution ()=default
	~CurlCurlExactSolution ()=default
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)

Static Public Member Functions
static void	RM (RealTensor T)

Private Attributes
const Real	k = pi

Static Private Attributes
static RealTensor	R

Detailed Description

Definition at line 26 of file curl_curl_exact_solution.h.

Constructor & Destructor Documentation

CurlCurlExactSolution() [1/2]

CurlCurlExactSolution::CurlCurlExactSolution ( )

default

~CurlCurlExactSolution() [1/2]

CurlCurlExactSolution::~CurlCurlExactSolution ( )

default

CurlCurlExactSolution() [2/2]

CurlCurlExactSolution::CurlCurlExactSolution ( )

default

~CurlCurlExactSolution() [2/2]

CurlCurlExactSolution::~CurlCurlExactSolution ( )

default

Member Function Documentation

curl()

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

inline

Definition at line 58 of file curl_curl_exact_solution.h.

References libMesh::Real.

  {
    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);
  }

forcing() [1/2]

RealGradient CurlCurlExactSolution::forcing ( Point  p )

inline

Definition at line 56 of file curl_curl_exact_solution.h.

Referenced by CurlCurlSystem::element_time_derivative(), and CurlCurlSystem::forcing().

  {
    return (2*k*k + 1)*operator()(p);
  }

forcing() [2/2]

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

inline

Definition at line 72 of file curl_curl_exact_solution.h.

References libMesh::Real.

  {
    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);
  }

grad() [1/2]

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

inline

Definition at line 41 of file curl_curl_exact_solution.h.

References libMesh::Real.

  {
    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);
  }

grad() [2/2]

RealTensor CurlCurlExactSolution::grad ( Point  p )

inline

Definition at line 43 of file curl_curl_exact_solution.h.

References libMesh::Real, and libMesh::TypeTensor< T >::transpose().

  {
    Point pp = R.transpose()*p;
    Real x = pp(0), y = pp(1);

    const Real dux_dx = -k*sin(k*x)*sin(k*y);
    const Real dux_dy =  k*cos(k*x)*cos(k*y);
    const Real duy_dx = -k*cos(k*x)*cos(k*y);
    const Real duy_dy =  k*sin(k*x)*sin(k*y);

    return R*RealTensor(dux_dx, dux_dy, Real(0), duy_dx, duy_dy)*R.transpose();
  }

operator()() [1/2]

RealGradient CurlCurlExactSolution::operator() ( Point  p )

inline

Definition at line 32 of file curl_curl_exact_solution.h.

References libMesh::Real.

  {
    Point pp = R.transpose()*p;
    Real x = pp(0), y = pp(1);

    const Real ux =  cos(k*x)*sin(k*y);
    const Real uy = -sin(k*x)*cos(k*y);

    return R*RealGradient(ux, uy);
  }

operator()() [2/2]

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

inline

Definition at line 32 of file curl_curl_exact_solution.h.

References libMesh::Real.

  {
    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);
  }

RM()

static void CurlCurlExactSolution::RM ( RealTensor  T )

inlinestatic

Definition at line 61 of file curl_curl_exact_solution.h.

Referenced by main().

  {
    R = T;
  }

Member Data Documentation

k

const Real CurlCurlExactSolution::k = pi

private

Definition at line 68 of file curl_curl_exact_solution.h.

R

RealTensor CurlCurlExactSolution::R

staticprivate

Definition at line 67 of file curl_curl_exact_solution.h.

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

• examples/vector_fe/vector_fe_ex3/curl_curl_exact_solution.h
• examples/vector_fe/vector_fe_ex3/vector_fe_ex3.C