void QGaussLobatto::init_3D(const ElemType type_in,
unsigned int p)
{
switch (type_in)
{
case HEX8:
case HEX20:
case HEX27:
{
// We compute the 3D quadrature rule as a tensor
// product of the 1D quadrature rule.
QGaussLobatto q1D(1, _order);
q1D.init(EDGE2, p);
tensor_product_hex(q1D);
return;
}
// We *could* fall back to a Gauss type rule for other types
// elements, but the assumption here is that the user has asked
// for a Gauss-Lobatto rule, i.e. a rule with integration points
// on the element boundary, for a reason.
default:
libmesh_error_msg("ERROR: Unsupported type: " << type_in);
}
}
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 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_3D(const ElemType type_in,
unsigned int)
{
#if LIBMESH_DIM == 3
//-----------------------------------------------------------------------
// 3D quadrature rules
switch (type_in)
{
//---------------------------------------------
// Hex quadrature rules
case HEX8:
case HEX20:
case HEX27:
{
// We compute the 3D quadrature rule as a tensor
// product of the 1D quadrature rule.
QSimpson q1D(1);
q1D.init(EDGE2);
tensor_product_hex( q1D );
return;
}
//---------------------------------------------
// Tetrahedral quadrature rules
case TET4:
case TET10:
{
// This rule is created by combining 8 subtets
// which use the trapezoidal rule. The weights
// may seem a bit odd, but they are correct,
// and should add up to 1/6, the volume of the
// reference tet. The points of this rule are
// at the nodal points of the TET10, allowing
// you to generate diagonal element stiffness
// matrices when using quadratic elements.
// It should be able to integrate something
// better than linears, but I'm not sure how
// high.
_points.resize(10);
_weights.resize(10);
_points[0](0) = 0.; _points[5](0) = .5;
_points[0](1) = 0.; _points[5](1) = .5;
_points[0](2) = 0.; _points[5](2) = 0.;
_points[1](0) = 1.; _points[6](0) = 0.;
_points[1](1) = 0.; _points[6](1) = .5;
_points[1](2) = 0.; _points[6](2) = 0.;
_points[2](0) = 0.; _points[7](0) = 0.;
_points[2](1) = 1.; _points[7](1) = 0.;
_points[2](2) = 0.; _points[7](2) = .5;
_points[3](0) = 0.; _points[8](0) = .5;
_points[3](1) = 0.; _points[8](1) = 0.;
_points[3](2) = 1.; _points[8](2) = .5;
_points[4](0) = .5; _points[9](0) = 0.;
_points[4](1) = 0.; _points[9](1) = .5;
_points[4](2) = 0.; _points[9](2) = .5;
_weights[0] = Real(1)/192;
_weights[1] = _weights[0];
_weights[2] = _weights[0];
_weights[3] = _weights[0];
_weights[4] = Real(14)/576;
_weights[5] = _weights[4];
_weights[6] = _weights[4];
_weights[7] = _weights[4];
_weights[8] = _weights[4];
_weights[9] = _weights[4];
return;
}
//---------------------------------------------
// Prism quadrature rules
case PRISM6:
case PRISM15:
case PRISM18:
{
// We compute the 3D quadrature rule as a tensor
// product of the 1D quadrature rule and a 2D
// triangle quadrature rule
QSimpson q1D(1);
QSimpson q2D(2);
// Initialize
q1D.init(EDGE2);
q2D.init(TRI3);
tensor_product_prism(q1D, q2D);
return;
}
//---------------------------------------------
// Unsupported type
default:
libmesh_error_msg("ERROR: Unsupported type: " << type_in);
}
#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
}
void QTrap::init_3D(const ElemType type_in,
unsigned int)
{
#if LIBMESH_DIM == 3
//-----------------------------------------------------------------------
// 3D quadrature rules
switch (type_in)
{
//---------------------------------------------
// Hex quadrature rules
case HEX8:
case HEX20:
case HEX27:
{
// We compute the 3D quadrature rule as a tensor
// product of the 1D quadrature rule.
QTrap q1D(1);
q1D.init(EDGE2);
tensor_product_hex( q1D );
return;
}
//---------------------------------------------
// Tetrahedral quadrature rules
case TET4:
case TET10:
{
_points.resize(4);
_weights.resize(4);
_points[0](0) = 0.;
_points[0](1) = 0.;
_points[0](2) = 0.;
_points[1](0) = 1.;
_points[1](1) = 0.;
_points[1](2) = 0.;
_points[2](0) = 0.;
_points[2](1) = 1.;
_points[2](2) = 0.;
_points[3](0) = 0.;
_points[3](1) = 0.;
_points[3](2) = 1.;
_weights[0] = .0416666666666666666666666666666666666666666667;
_weights[1] = _weights[0];
_weights[2] = _weights[0];
_weights[3] = _weights[0];
return;
}
//---------------------------------------------
// Prism quadrature rules
case PRISM6:
case PRISM15:
case PRISM18:
{
// We compute the 3D quadrature rule as a tensor
// product of the 1D quadrature rule and a 2D
// triangle quadrature rule
QTrap q1D(1);
QTrap q2D(2);
// Initialize
q1D.init(EDGE2);
q2D.init(TRI3);
tensor_product_prism(q1D, q2D);
return;
}
//---------------------------------------------
// Unsupported type
default:
{
libMesh::err << "ERROR: Unsupported type: " << type_in << std::endl;
libmesh_error();
}
}
libmesh_error();
return;
#endif
}
