fe_test.h File Reference

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Classes
class	SkewFunc
class	FETestBase< order, family, elem_type, build_nx >
class	FETest< order, family, elem_type >

Functions
Number	linear_test (const Point &p, const Parameters &, const std::string &, const std::string &)
Gradient	linear_test_grad (const Point &, const Parameters &, const std::string &, const std::string &)
Number	quadratic_test (const Point &p, const Parameters &, const std::string &, const std::string &)
Gradient	quadratic_test_grad (const Point &p, const Parameters &, const std::string &, const std::string &)
Number	fe_cubic_test (const Point &p, const Parameters &, const std::string &, const std::string &)
Gradient	fe_cubic_test_grad (const Point &p, const Parameters &, const std::string &, const std::string &)
Number	fe_quartic_test (const Point &p, const Parameters &, const std::string &, const std::string &)
Gradient	fe_quartic_test_grad (const Point &p, const Parameters &, const std::string &, const std::string &)
Number	rational_test (const Point &p, const Parameters &, const std::string &, const std::string &)
Gradient	rational_test_grad (const Point &p, const Parameters &, const std::string &, const std::string &)

Variables
static const Real	rational_w = 0.75

Function Documentation

fe_cubic_test()

Number fe_cubic_test ( const Point &  p, const Parameters &  , const std::string &  , const std::string &    )

inline

Definition at line 128 of file fe_test.h.

References libMesh::Real.

Referenced by FETestBase< order, family, elem_type, 1 >::setUp(), FESideTest< order, family, elem_type >::testU(), and FETest< order, family, elem_type >::testU().

{
  const Real & x = p(0);
  const Real & y = (LIBMESH_DIM > 1) ? p(1) : 0;
  const Real & z = (LIBMESH_DIM > 2) ? p(2) : 0;

  return x*(1-x)*(1-x) + x*x*(1-y) + x*(1-y)*(1-z) + y*(1-y)*z + z*(1-z)*(1-z);
}

fe_cubic_test_grad()

Gradient fe_cubic_test_grad ( const Point &  p, const Parameters &  , const std::string &  , const std::string &    )

inline

Definition at line 141 of file fe_test.h.

References libMesh::Real.

Referenced by FETestBase< order, family, elem_type, 1 >::setUp(), and FETestBase< order, family, elem_type, 1 >::true_gradient().

{
  const Real & x = p(0);
  const Real & y = (LIBMESH_DIM > 1) ? p(1) : 0;
  const Real & z = (LIBMESH_DIM > 2) ? p(2) : 0;

  Gradient grad = 3*x*x-4*x+1 + 2*x*(1-y) + (1-y)*(1-z);
  if (LIBMESH_DIM > 1)
    grad(1) = -x*x - x*(1-z) + (1-2*y)*z;
  if (LIBMESH_DIM > 2)
    grad(2) = -x*(1-y) + y*(1-y) + 3*z*z-4*z+1;

  return grad;
}

fe_quartic_test()

Number fe_quartic_test ( const Point &  p, const Parameters &  , const std::string &  , const std::string &    )

inline

Definition at line 161 of file fe_test.h.

References libMesh::Real.

Referenced by FETestBase< order, family, elem_type, 1 >::setUp(), FESideTest< order, family, elem_type >::testU(), and FETest< order, family, elem_type >::testU().

{
  const Real & x = p(0);
  const Real & y = (LIBMESH_DIM > 1) ? p(1) : 0;
  const Real & z = (LIBMESH_DIM > 2) ? p(2) : 0;

  return x*x*(1-x)*(1-x) + x*x*z*(1-y) + x*(1-x)*(1-y)*(1-z) + (1-x)*y*(1-y)*z + z*z*(1-z)*(1-z);
}

fe_quartic_test_grad()

Gradient fe_quartic_test_grad ( const Point &  p, const Parameters &  , const std::string &  , const std::string &    )

inline

Definition at line 174 of file fe_test.h.

References libMesh::Real.

Referenced by FETestBase< order, family, elem_type, 1 >::setUp(), and FETestBase< order, family, elem_type, 1 >::true_gradient().

{
  const Real & x = p(0);
  const Real & y = (LIBMESH_DIM > 1) ? p(1) : 0;
  const Real & z = (LIBMESH_DIM > 2) ? p(2) : 0;

  Gradient grad = 4*x*x*x-6*x*x+2*x + 2*x*z*(1-y) + (1-2*x)*(1-y)*(1-z) - y*(1-y)*z;
  if (LIBMESH_DIM > 1)
    grad(1) = -x*x*z - x*(1-x)*(1-z) + (1-x)*(1-2*y)*z;
  if (LIBMESH_DIM > 2)
    grad(2) = x*x*(1-y) - x*(1-x)*(1-y) + (1-x)*y*(1-y) + 4*z*z*z-6*z*z+2*z;

  return grad;
}

linear_test()

Number linear_test ( const Point &  p, const Parameters &  , const std::string &  , const std::string &    )

inline

Definition at line 66 of file fe_test.h.

References libMesh::Real.

Referenced by FETestBase< order, family, elem_type, 1 >::setUp().

{
  const Real & x = p(0);
  const Real & y = (LIBMESH_DIM > 1) ? p(1) : 0;
  const Real & z = (LIBMESH_DIM > 2) ? p(2) : 0;

  return x + 0.25*y + 0.0625*z;
}

linear_test_grad()

Gradient linear_test_grad ( const Point &  , const Parameters &  , const std::string &  , const std::string &    )

inline

Definition at line 79 of file fe_test.h.

Referenced by FETestBase< order, family, elem_type, 1 >::setUp().

{
  Gradient grad = 1;
  if (LIBMESH_DIM > 1)
    grad(1) = 0.25;
  if (LIBMESH_DIM > 2)
    grad(2) = 0.0625;

  return grad;
}

quadratic_test()

Number quadratic_test ( const Point &  p, const Parameters &  , const std::string &  , const std::string &    )

inline

Definition at line 95 of file fe_test.h.

References libMesh::Real.

Referenced by FETestBase< order, family, elem_type, 1 >::setUp().

{
  const Real & x = p(0);
  const Real & y = (LIBMESH_DIM > 1) ? p(1) : 0;
  const Real & z = (LIBMESH_DIM > 2) ? p(2) : 0;

  return x*x + 0.5*y*y + 0.25*z*z + 0.125*x*y + 0.0625*x*z + 0.03125*y*z;
}

quadratic_test_grad()

Gradient quadratic_test_grad ( const Point &  p, const Parameters &  , const std::string &  , const std::string &    )

inline

Definition at line 108 of file fe_test.h.

References libMesh::Real.

Referenced by FETestBase< order, family, elem_type, 1 >::setUp().

{
  const Real & x = p(0);
  const Real & y = (LIBMESH_DIM > 1) ? p(1) : 0;
  const Real & z = (LIBMESH_DIM > 2) ? p(2) : 0;

  Gradient grad = 2*x + 0.125*y + 0.0625*z;
  if (LIBMESH_DIM > 1)
    grad(1) = y + 0.125*x + 0.03125*z;
  if (LIBMESH_DIM > 2)
    grad(2) = 0.5*z + 0.0625*x + 0.03125*y;

  return grad;
}

rational_test()

Number rational_test ( const Point &  p, const Parameters &  , const std::string &  , const std::string &    )

inline

Definition at line 200 of file fe_test.h.

References rational_w, and libMesh::Real.

Referenced by FETestBase< order, family, elem_type, 1 >::setUp(), FESideTest< order, family, elem_type >::testU(), and FETest< order, family, elem_type >::testU().

{
  const Real & x = p(0);
  const Real & y = (LIBMESH_DIM > 1) ? p(1) : 0;
  const Real & z = (LIBMESH_DIM > 2) ? p(2) : 0;

  const Real denom = ((1-x)*(1-x)+x*x+2*rational_w*x*(1-x))*
                     ((1-y)*(1-y)+y*y+2*rational_w*y*(1-y))*
                     ((1-z)*(1-z)+z*z+2*rational_w*z*(1-z));

  return (x + 0.25*y + 0.0625*z)/denom;
}

rational_test_grad()

Gradient rational_test_grad ( const Point &  p, const Parameters &  , const std::string &  , const std::string &    )

inline

Definition at line 217 of file fe_test.h.

References rational_w, and libMesh::Real.

Referenced by FETestBase< order, family, elem_type, 1 >::setUp(), and FETestBase< order, family, elem_type, 1 >::true_gradient().

{
  const Real & x = p(0);
  const Real & y = (LIBMESH_DIM > 1) ? p(1) : 0;
  const Real & z = (LIBMESH_DIM > 2) ? p(2) : 0;

  const Real xpoly = (1-x)*(1-x)+x*x+2*rational_w*x*(1-x);
  const Real xderiv = -2*(1-x)+2*x+2*rational_w*(1-2*x);
  const Real ypoly = (1-y)*(1-y)+y*y+2*rational_w*y*(1-y);
  const Real yderiv = -2*(1-y)+2*y+2*rational_w*(1-2*y);
  const Real zpoly = (1-z)*(1-z)+z*z+2*rational_w*z*(1-z);
  const Real zderiv = -2*(1-z)+2*z+2*rational_w*(1-2*z);

  const Real denom = xpoly * ypoly * zpoly;

  const Real numer = (x + 0.25*y + 0.0625*z);

  Gradient grad_n = 1, grad_d = xderiv * ypoly * zpoly;
  if (LIBMESH_DIM > 1)
    {
      grad_n(1) = 0.25;
      grad_d(1) = xpoly * yderiv * zpoly;
    }
  if (LIBMESH_DIM > 2)
    {
      grad_n(2) = 0.0625;
      grad_d(2) = xpoly * ypoly * zderiv;
    }

  Gradient grad = (grad_n - numer * grad_d / denom) / denom;

  return grad;
}

Variable Documentation

rational_w

const Real rational_w = 0.75

static

Definition at line 197 of file fe_test.h.

Referenced by rational_test(), rational_test_grad(), and FETestBase< order, family, elem_type, 1 >::setUp().