GradDivExactSolution Class Reference

#include <grad_div_exact_solution.h>

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

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 grad_div_exact_solution.h.

Constructor & Destructor Documentation

GradDivExactSolution()

GradDivExactSolution::GradDivExactSolution ( )

default

~GradDivExactSolution()

GradDivExactSolution::~GradDivExactSolution ( )

default

Member Function Documentation

forcing()

RealGradient GradDivExactSolution::forcing ( Point  p )

inline

Definition at line 56 of file grad_div_exact_solution.h.

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

References k, and operator()().

Referenced by assemble_graddiv().

grad()

RealTensor GradDivExactSolution::grad ( Point  p )

inline

Definition at line 43 of file grad_div_exact_solution.h.

  {
    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 = dux_dy;
    const Real duy_dy = dux_dx;
 
    return R*RealTensor(dux_dx, dux_dy, Real(0), duy_dx, duy_dy)*R.transpose()/R.det();
  }

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

Referenced by SolutionGradient< dim >::component(), and SolutionGradient< dim >::operator()().

operator()()

RealGradient GradDivExactSolution::operator() ( Point  p )

inline

Definition at line 32 of file grad_div_exact_solution.h.

  {
    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)/R.det();
  }

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

Referenced by forcing().

RM()

static void GradDivExactSolution::RM ( RealTensor  T )

inlinestatic

Definition at line 61 of file grad_div_exact_solution.h.

  {
    R = T;
  }

References R.

Referenced by main().

Member Data Documentation

k

const Real GradDivExactSolution::k = pi

private

Definition at line 68 of file grad_div_exact_solution.h.

Referenced by forcing(), grad(), and operator()().

R

RealTensor GradDivExactSolution::R

staticprivate

Definition at line 67 of file grad_div_exact_solution.h.

Referenced by grad(), operator()(), and RM().

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

• examples/vector_fe/vector_fe_ex10/grad_div_exact_solution.h
• examples/vector_fe/vector_fe_ex10/vector_fe_ex10.C