void QGrid::init_2D(const ElemType type_in,
unsigned int)
{
#if LIBMESH_DIM > 1
//-----------------------------------------------------------------------
// 2D quadrature rules
// We ignore p - the grid rule is just for experimentation
switch (type_in)
{
//---------------------------------------------
// Quadrilateral quadrature rules
case QUAD4:
case QUAD8:
case QUAD9:
{
// We compute the 2D quadrature rule as a tensor
// product of the 1D quadrature rule.
QGrid q1D(1,_order);
q1D.init(EDGE2);
tensor_product_quad( q1D );
return;
}
//---------------------------------------------
// Triangle quadrature rules
case TRI3:
case TRI6:
{
const unsigned int np = (_order + 1)*(_order + 2)/2;
const Real weight = 0.5/np;
const Real dx = 1.0/(_order+1);
_points.resize(np);
_weights.resize(np);
unsigned int pt = 0;
for (int i = 0; i != _order + 1; ++i)
{
for (int j = 0; j != _order + 1 - i; ++j)
{
_points[pt](0) = (i+0.5)*dx;
_points[pt](1) = (j+0.5)*dx;
_weights[pt] = weight;
pt++;
}
}
return;
}
//---------------------------------------------
// Unsupported type
default:
{
libMesh::err << "Element type not supported!:" << type_in << std::endl;
libmesh_error();
}
}
libmesh_error();
return;
#endif
}
void QSimpson::init_2D(const ElemType type_in,
unsigned int)
{
#if LIBMESH_DIM > 1
//-----------------------------------------------------------------------
// 2D quadrature rules
switch (type_in)
{
//---------------------------------------------
// Quadrilateral quadrature rules
case QUAD4:
case QUAD8:
case QUAD9:
{
// We compute the 2D quadrature rule as a tensor
// product of the 1D quadrature rule.
QSimpson q1D(1);
q1D.init(EDGE2);
tensor_product_quad( q1D );
return;
}
//---------------------------------------------
// Triangle quadrature rules
case TRI3:
case TRI6:
{
// I'm not sure if you would call this Simpson's
// rule for triangles. What it *Really* is is
// four trapezoidal rules combined to give a six
// point rule. The points lie at the nodal locations
// of the TRI6, so you can get diagonal element
// stiffness matrix entries for quadratic elements.
// This rule should be able to integrate a little
// better than linears exactly.
_points.resize(6);
_weights.resize(6);
_points[0](0) = 0.;
_points[0](1) = 0.;
_points[1](0) = 1.;
_points[1](1) = 0.;
_points[2](0) = 0.;
_points[2](1) = 1.;
_points[3](0) = 0.5;
_points[3](1) = 0.;
_points[4](0) = 0.;
_points[4](1) = 0.5;
_points[5](0) = 0.5;
_points[5](1) = 0.5;
_weights[0] = 0.041666666666666666666666666667; // 1./24.
_weights[1] = 0.041666666666666666666666666667; // 1./24.
_weights[2] = 0.041666666666666666666666666667; // 1./24.
_weights[3] = 0.125; // 1./8.
_weights[4] = 0.125; // 1./8.
_weights[5] = 0.125; // 1./8.
return;
}
//---------------------------------------------
// Unsupported type
default:
{
libMesh::err << "Element type not supported!:" << type_in << std::endl;
libmesh_error();
}
}
libmesh_error();
return;
#endif
}
void QTrap::init_2D(const ElemType type_in,
unsigned int)
{
#if LIBMESH_DIM > 1
//-----------------------------------------------------------------------
// 2D quadrature rules
switch (type_in)
{
//---------------------------------------------
// Quadrilateral quadrature rules
case QUAD4:
case QUAD8:
case QUAD9:
{
// We compute the 2D quadrature rule as a tensor
// product of the 1D quadrature rule.
QTrap q1D(1);
q1D.init(EDGE2);
tensor_product_quad( q1D );
return;
}
//---------------------------------------------
// Triangle quadrature rules
case TRI3:
case TRI6:
{
_points.resize(3);
_weights.resize(3);
_points[0](0) = 0.;
_points[0](1) = 0.;
_points[1](0) = 1.;
_points[1](1) = 0.;
_points[2](0) = 0.;
_points[2](1) = 1.;
_weights[0] = 1./6.;
_weights[1] = 1./6.;
_weights[2] = 1./6.;
return;
}
//---------------------------------------------
// Unsupported type
default:
{
libMesh::err << "Element type not supported!:" << type_in << std::endl;
libmesh_error();
}
}
libmesh_error();
return;
#endif
}
