Real InfFE<Dim,T_radial,T_map>::shape(const FEType & fet,
const Elem * inf_elem,
const unsigned int i,
const Point & p)
{
libmesh_assert(inf_elem);
libmesh_assert_not_equal_to (Dim, 0);
#ifdef DEBUG
// this makes only sense when used for mapping
if ((T_radial != INFINITE_MAP) && !_warned_for_shape)
{
libMesh::err << "WARNING: InfFE<Dim,T_radial,T_map>::shape(...) does _not_" << std::endl
<< " return the correct trial function! Use " << std::endl
<< " InfFE<Dim,T_radial,T_map>::compute_data(..) instead!"
<< std::endl;
_warned_for_shape = true;
}
#endif
const Order o_radial (fet.radial_order);
const Real v (p(Dim-1));
UniquePtr<const Elem> base_el (inf_elem->build_side_ptr(0));
unsigned int i_base, i_radial;
compute_shape_indices(fet, inf_elem->type(), i, i_base, i_radial);
if (Dim > 1)
return FEInterface::shape(Dim-1, fet, base_el.get(), i_base, p)
* InfFE<Dim,T_radial,T_map>::eval(v, o_radial, i_radial)
* InfFE<Dim,T_radial,T_map>::Radial::decay(v);
else
return InfFE<Dim,T_radial,T_map>::eval(v, o_radial, i_radial)
* InfFE<Dim,T_radial,T_map>::Radial::decay(v);
}
Real InfFE<Dim,T_radial,T_map>::shape(const FEType & fet,
const ElemType inf_elem_type,
const unsigned int i,
const Point & p)
{
libmesh_assert_not_equal_to (Dim, 0);
#ifdef DEBUG
// this makes only sense when used for mapping
if ((T_radial != INFINITE_MAP) && !_warned_for_shape)
{
libMesh::err << "WARNING: InfFE<Dim,T_radial,T_map>::shape(...) does _not_" << std::endl
<< " return the correct trial function! Use " << std::endl
<< " InfFE<Dim,T_radial,T_map>::compute_data(..) instead!"
<< std::endl;
_warned_for_shape = true;
}
#endif
const ElemType base_et (Base::get_elem_type(inf_elem_type));
const Order o_radial (fet.radial_order);
const Real v (p(Dim-1));
unsigned int i_base, i_radial;
compute_shape_indices(fet, inf_elem_type, i, i_base, i_radial);
//TODO:[SP/DD] exp(ikr) is still missing here!
if (Dim > 1)
return FEInterface::shape(Dim-1, fet, base_et, i_base, p)
* InfFE<Dim,T_radial,T_map>::eval(v, o_radial, i_radial)
* InfFE<Dim,T_radial,T_map>::Radial::decay(v);
else
return InfFE<Dim,T_radial,T_map>::eval(v, o_radial, i_radial)
* InfFE<Dim,T_radial,T_map>::Radial::decay(v);
}
void InfFE<Dim,T_radial,T_map>::init_shape_functions(const Elem * inf_elem)
{
libmesh_assert(inf_elem);
// Start logging the radial shape function initialization
START_LOG("init_shape_functions()", "InfFE");
// -----------------------------------------------------------------
// fast access to some const int's for the radial data
const unsigned int n_radial_mapping_sf =
cast_int<unsigned int>(radial_map.size());
const unsigned int n_radial_approx_sf =
cast_int<unsigned int>(mode.size());
const unsigned int n_radial_qp =
cast_int<unsigned int>(som.size());
// -----------------------------------------------------------------
// initialize most of the things related to mapping
// The element type and order to use in the base map
const Order base_mapping_order ( base_elem->default_order() );
const ElemType base_mapping_elem_type ( base_elem->type() );
// the number of base shape functions used to construct the map
// (Lagrange shape functions are used for mapping in the base)
unsigned int n_base_mapping_shape_functions = Base::n_base_mapping_sf(base_mapping_elem_type,
base_mapping_order);
const unsigned int n_total_mapping_shape_functions =
n_radial_mapping_sf * n_base_mapping_shape_functions;
// -----------------------------------------------------------------
// initialize most of the things related to physical approximation
unsigned int n_base_approx_shape_functions;
if (Dim > 1)
n_base_approx_shape_functions = base_fe->n_shape_functions();
else
n_base_approx_shape_functions = 1;
const unsigned int n_total_approx_shape_functions =
n_radial_approx_sf * n_base_approx_shape_functions;
// update class member field
_n_total_approx_sf = n_total_approx_shape_functions;
// The number of the base quadrature points.
const unsigned int n_base_qp = base_qrule->n_points();
// The total number of quadrature points.
const unsigned int n_total_qp = n_radial_qp * n_base_qp;
// update class member field
_n_total_qp = n_total_qp;
// -----------------------------------------------------------------
// initialize the node and shape numbering maps
{
// these vectors work as follows: the i-th entry stores
// the associated base/radial node number
_radial_node_index.resize (n_total_mapping_shape_functions);
_base_node_index.resize (n_total_mapping_shape_functions);
// similar for the shapes: the i-th entry stores
// the associated base/radial shape number
_radial_shape_index.resize (n_total_approx_shape_functions);
_base_shape_index.resize (n_total_approx_shape_functions);
const ElemType inf_elem_type (inf_elem->type());
// fill the node index map
for (unsigned int n=0; n<n_total_mapping_shape_functions; n++)
{
compute_node_indices (inf_elem_type,
n,
_base_node_index[n],
_radial_node_index[n]);
libmesh_assert_less (_base_node_index[n], n_base_mapping_shape_functions);
libmesh_assert_less (_radial_node_index[n], n_radial_mapping_sf);
}
// fill the shape index map
for (unsigned int n=0; n<n_total_approx_shape_functions; n++)
{
compute_shape_indices (this->fe_type,
inf_elem_type,
n,
_base_shape_index[n],
_radial_shape_index[n]);
libmesh_assert_less (_base_shape_index[n], n_base_approx_shape_functions);
libmesh_assert_less (_radial_shape_index[n], n_radial_approx_sf);
}
}
// -----------------------------------------------------------------
// resize the base data fields
dist.resize(n_base_mapping_shape_functions);
// -----------------------------------------------------------------
// resize the total data fields
// the phase term varies with xi, eta and zeta(v): store it for _all_ qp
//
// when computing the phase, we need the base approximations
// therefore, initialize the phase here, but evaluate it
// in combine_base_radial().
//
// the weight, though, is only needed at the radial quadrature points, n_radial_qp.
// but for a uniform interface to the protected data fields
// the weight data field (which are accessible from the outside) are expanded to n_total_qp.
weight.resize (n_total_qp);
dweightdv.resize (n_total_qp);
dweight.resize (n_total_qp);
dphase.resize (n_total_qp);
dphasedxi.resize (n_total_qp);
dphasedeta.resize (n_total_qp);
dphasedzeta.resize (n_total_qp);
// this vector contains the integration weights for the combined quadrature rule
_total_qrule_weights.resize(n_total_qp);
// -----------------------------------------------------------------
// InfFE's data fields phi, dphi, dphidx, phi_map etc hold the _total_
// shape and mapping functions, respectively
{
phi.resize (n_total_approx_shape_functions);
dphi.resize (n_total_approx_shape_functions);
dphidx.resize (n_total_approx_shape_functions);
dphidy.resize (n_total_approx_shape_functions);
dphidz.resize (n_total_approx_shape_functions);
dphidxi.resize (n_total_approx_shape_functions);
#ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
libmesh_do_once(libMesh::err << "Second derivatives for Infinite elements"
<< " are not yet implemented!"
<< std::endl);
d2phi.resize (n_total_approx_shape_functions);
d2phidx2.resize (n_total_approx_shape_functions);
d2phidxdy.resize (n_total_approx_shape_functions);
d2phidxdz.resize (n_total_approx_shape_functions);
d2phidy2.resize (n_total_approx_shape_functions);
d2phidydz.resize (n_total_approx_shape_functions);
d2phidz2.resize (n_total_approx_shape_functions);
d2phidxi2.resize (n_total_approx_shape_functions);
if (Dim > 1)
{
d2phidxideta.resize (n_total_approx_shape_functions);
d2phideta2.resize (n_total_approx_shape_functions);
}
if (Dim > 2)
{
d2phidetadzeta.resize (n_total_approx_shape_functions);
d2phidxidzeta.resize (n_total_approx_shape_functions);
d2phidzeta2.resize (n_total_approx_shape_functions);
}
#endif // ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
if (Dim > 1)
dphideta.resize (n_total_approx_shape_functions);
if (Dim == 3)
dphidzeta.resize (n_total_approx_shape_functions);
std::vector<std::vector<Real> > & phi_map = this->_fe_map->get_phi_map();
std::vector<std::vector<Real> > & dphidxi_map = this->_fe_map->get_dphidxi_map();
phi_map.resize (n_total_mapping_shape_functions);
dphidxi_map.resize (n_total_mapping_shape_functions);
#ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
std::vector<std::vector<Real> > & d2phidxi2_map = this->_fe_map->get_d2phidxi2_map();
d2phidxi2_map.resize (n_total_mapping_shape_functions);
if (Dim > 1)
{
std::vector<std::vector<Real> > & d2phidxideta_map = this->_fe_map->get_d2phidxideta_map();
std::vector<std::vector<Real> > & d2phideta2_map = this->_fe_map->get_d2phideta2_map();
d2phidxideta_map.resize (n_total_mapping_shape_functions);
d2phideta2_map.resize (n_total_mapping_shape_functions);
}
if (Dim == 3)
{
std::vector<std::vector<Real> > & d2phidxidzeta_map = this->_fe_map->get_d2phidxidzeta_map();
std::vector<std::vector<Real> > & d2phidetadzeta_map = this->_fe_map->get_d2phidetadzeta_map();
std::vector<std::vector<Real> > & d2phidzeta2_map = this->_fe_map->get_d2phidzeta2_map();
d2phidxidzeta_map.resize (n_total_mapping_shape_functions);
d2phidetadzeta_map.resize (n_total_mapping_shape_functions);
d2phidzeta2_map.resize (n_total_mapping_shape_functions);
}
#endif // ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
if (Dim > 1)
{
std::vector<std::vector<Real> > & dphideta_map = this->_fe_map->get_dphideta_map();
dphideta_map.resize (n_total_mapping_shape_functions);
}
if (Dim == 3)
{
std::vector<std::vector<Real> > & dphidzeta_map = this->_fe_map->get_dphidzeta_map();
dphidzeta_map.resize (n_total_mapping_shape_functions);
}
}
// -----------------------------------------------------------------
// collect all the for loops, where inner vectors are
// resized to the appropriate number of quadrature points
{
for (unsigned int i=0; i<n_total_approx_shape_functions; i++)
{
phi[i].resize (n_total_qp);
dphi[i].resize (n_total_qp);
dphidx[i].resize (n_total_qp);
dphidy[i].resize (n_total_qp);
dphidz[i].resize (n_total_qp);
dphidxi[i].resize (n_total_qp);
#ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
d2phi[i].resize (n_total_qp);
d2phidx2[i].resize (n_total_qp);
d2phidxdy[i].resize (n_total_qp);
d2phidxdz[i].resize (n_total_qp);
d2phidy2[i].resize (n_total_qp);
d2phidydz[i].resize (n_total_qp);
d2phidy2[i].resize (n_total_qp);
d2phidxi2[i].resize (n_total_qp);
if (Dim > 1)
{
d2phidxideta[i].resize (n_total_qp);
d2phideta2[i].resize (n_total_qp);
}
if (Dim > 2)
{
d2phidxidzeta[i].resize (n_total_qp);
d2phidetadzeta[i].resize (n_total_qp);
d2phidzeta2[i].resize (n_total_qp);
}
#endif // ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
if (Dim > 1)
dphideta[i].resize (n_total_qp);
if (Dim == 3)
dphidzeta[i].resize (n_total_qp);
}
for (unsigned int i=0; i<n_total_mapping_shape_functions; i++)
{
std::vector<std::vector<Real> > & phi_map = this->_fe_map->get_phi_map();
std::vector<std::vector<Real> > & dphidxi_map = this->_fe_map->get_dphidxi_map();
phi_map[i].resize (n_total_qp);
dphidxi_map[i].resize (n_total_qp);
#ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
std::vector<std::vector<Real> > & d2phidxi2_map = this->_fe_map->get_d2phidxi2_map();
d2phidxi2_map[i].resize (n_total_qp);
if (Dim > 1)
{
std::vector<std::vector<Real> > & d2phidxideta_map = this->_fe_map->get_d2phidxideta_map();
std::vector<std::vector<Real> > & d2phideta2_map = this->_fe_map->get_d2phideta2_map();
d2phidxideta_map[i].resize (n_total_qp);
d2phideta2_map[i].resize (n_total_qp);
}
if (Dim > 2)
{
std::vector<std::vector<Real> > & d2phidxidzeta_map = this->_fe_map->get_d2phidxidzeta_map();
std::vector<std::vector<Real> > & d2phidetadzeta_map = this->_fe_map->get_d2phidetadzeta_map();
std::vector<std::vector<Real> > & d2phidzeta2_map = this->_fe_map->get_d2phidzeta2_map();
d2phidxidzeta_map[i].resize (n_total_qp);
d2phidetadzeta_map[i].resize (n_total_qp);
d2phidzeta2_map[i].resize (n_total_qp);
}
#endif // ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
if (Dim > 1)
{
std::vector<std::vector<Real> > & dphideta_map = this->_fe_map->get_dphideta_map();
dphideta_map[i].resize (n_total_qp);
}
if (Dim == 3)
{
std::vector<std::vector<Real> > & dphidzeta_map = this->_fe_map->get_dphidzeta_map();
dphidzeta_map[i].resize (n_total_qp);
}
}
}
{
// -----------------------------------------------------------------
// (a) compute scalar values at _all_ quadrature points -- for uniform
// access from the outside to these fields
// (b) form a std::vector<Real> which contains the appropriate weights
// of the combined quadrature rule!
const std::vector<Point> & radial_qp = radial_qrule->get_points();
libmesh_assert_equal_to (radial_qp.size(), n_radial_qp);
const std::vector<Real> & radial_qw = radial_qrule->get_weights();
const std::vector<Real> & base_qw = base_qrule->get_weights();
libmesh_assert_equal_to (radial_qw.size(), n_radial_qp);
libmesh_assert_equal_to (base_qw.size(), n_base_qp);
for (unsigned int rp=0; rp<n_radial_qp; rp++)
for (unsigned int bp=0; bp<n_base_qp; bp++)
{
weight [ bp+rp*n_base_qp ] = Radial::D (radial_qp[rp](0));
dweightdv[ bp+rp*n_base_qp ] = Radial::D_deriv (radial_qp[rp](0));
_total_qrule_weights[ bp+rp*n_base_qp ] = radial_qw[rp] * base_qw[bp];
}
}
/**
* Stop logging the radial shape function initialization
*/
STOP_LOG("init_shape_functions()", "InfFE");
}
void InfFE<Dim,T_radial,T_map>::compute_data(const FEType & fet,
const Elem * inf_elem,
FEComputeData & data)
{
libmesh_assert(inf_elem);
libmesh_assert_not_equal_to (Dim, 0);
const Order o_radial (fet.radial_order);
const Order radial_mapping_order (Radial::mapping_order());
const Point & p (data.p);
const Real v (p(Dim-1));
UniquePtr<const Elem> base_el (inf_elem->build_side_ptr(0));
/*
* compute \p interpolated_dist containing the mapping-interpolated
* distance of the base point to the origin. This is the same
* for all shape functions. Set \p interpolated_dist to 0, it
* is added to.
*/
Real interpolated_dist = 0.;
switch (Dim)
{
case 1:
{
libmesh_assert_equal_to (inf_elem->type(), INFEDGE2);
interpolated_dist = Point(inf_elem->point(0) - inf_elem->point(1)).size();
break;
}
case 2:
{
const unsigned int n_base_nodes = base_el->n_nodes();
const Point origin = inf_elem->origin();
const Order base_mapping_order (base_el->default_order());
const ElemType base_mapping_elem_type (base_el->type());
// interpolate the base nodes' distances
for (unsigned int n=0; n<n_base_nodes; n++)
interpolated_dist += Point(base_el->point(n) - origin).size()
* FE<1,LAGRANGE>::shape (base_mapping_elem_type, base_mapping_order, n, p);
break;
}
case 3:
{
const unsigned int n_base_nodes = base_el->n_nodes();
const Point origin = inf_elem->origin();
const Order base_mapping_order (base_el->default_order());
const ElemType base_mapping_elem_type (base_el->type());
// interpolate the base nodes' distances
for (unsigned int n=0; n<n_base_nodes; n++)
interpolated_dist += Point(base_el->point(n) - origin).size()
* FE<2,LAGRANGE>::shape (base_mapping_elem_type, base_mapping_order, n, p);
break;
}
default:
libmesh_error_msg("Unknown Dim = " << Dim);
}
#ifdef LIBMESH_USE_COMPLEX_NUMBERS
// assumption on time-harmonic behavior
const short int sign (-1);
// the wave number
const Real wavenumber = 2. * libMesh::pi * data.frequency / data.speed;
// the exponent for time-harmonic behavior
const Real exponent = sign /* +1. or -1. */
* wavenumber /* k */
* interpolated_dist /* together with next line: */
* InfFE<Dim,INFINITE_MAP,T_map>::eval(v, radial_mapping_order, 1); /* phase(s,t,v) */
const Number time_harmonic = Number(cos(exponent), sin(exponent)); /* e^(sign*i*k*phase(s,t,v)) */
/*
* compute \p shape for all dof in the element
*/
if (Dim > 1)
{
const unsigned int n_dof = n_dofs (fet, inf_elem->type());
data.shape.resize(n_dof);
for (unsigned int i=0; i<n_dof; i++)
{
// compute base and radial shape indices
unsigned int i_base, i_radial;
compute_shape_indices(fet, inf_elem->type(), i, i_base, i_radial);
data.shape[i] = (InfFE<Dim,T_radial,T_map>::Radial::decay(v) /* (1.-v)/2. in 3D */
* FEInterface::shape(Dim-1, fet, base_el.get(), i_base, p) /* S_n(s,t) */
* InfFE<Dim,T_radial,T_map>::eval(v, o_radial, i_radial)) /* L_n(v) */
* time_harmonic; /* e^(sign*i*k*phase(s,t,v) */
}
}
else
libmesh_error_msg("compute_data() for 1-dimensional InfFE not implemented.");
#else
const Real speed = data.speed;
/*
* This is quite weird: the phase is actually
* a measure how @e advanced the pressure is that
* we compute. In other words: the further away
* the node \p data.p is, the further we look into
* the future...
*/
data.phase = interpolated_dist /* phase(s,t,v)/c */
* InfFE<Dim,INFINITE_MAP,T_map>::eval(v, radial_mapping_order, 1) / speed;
if (Dim > 1)
{
const unsigned int n_dof = n_dofs (fet, inf_elem->type());
data.shape.resize(n_dof);
for (unsigned int i=0; i<n_dof; i++)
{
// compute base and radial shape indices
unsigned int i_base, i_radial;
compute_shape_indices(fet, inf_elem->type(), i, i_base, i_radial);
data.shape[i] = InfFE<Dim,T_radial,T_map>::Radial::decay(v) /* (1.-v)/2. in 3D */
* FEInterface::shape(Dim-1, fet, base_el.get(), i_base, p) /* S_n(s,t) */
* InfFE<Dim,T_radial,T_map>::eval(v, o_radial, i_radial); /* L_n(v) */
}
}
else
libmesh_error_msg("compute_data() for 1-dimensional InfFE not implemented.");
#endif
}
