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// ---------------------------------------------------------------------
//
// Copyright (C) 2004 - 2015 by the deal.II authors
//
// This file is part of the deal.II library.
//
// The deal.II library is free software; you can use it, redistribute
// it, and/or modify it under the terms of the GNU Lesser General
// Public License as published by the Free Software Foundation; either
// version 2.1 of the License, or (at your option) any later version.
// The full text of the license can be found in the file LICENSE at
// the top level of the deal.II distribution.
//
// ---------------------------------------------------------------------
#include <deal.II/base/geometry_info.h>
#include <deal.II/base/polynomials_bdm.h>
#include <deal.II/base/polynomial_space.h>
#include <deal.II/base/quadrature_lib.h>
#include <iostream>
#include <iomanip>
DEAL_II_NAMESPACE_OPEN
template <int dim>
PolynomialsBDM<dim>::PolynomialsBDM (const unsigned int k)
:
polynomial_space (Polynomials::Legendre::generate_complete_basis(k)),
monomials((dim==2) ? (1) : (k+2)),
n_pols(compute_n_pols(k)),
p_values(polynomial_space.n()),
p_grads(polynomial_space.n()),
p_grad_grads(polynomial_space.n())
{
switch (dim)
{
case 2:
monomials[0] = Polynomials::Monomial<double> (k+1);
break;
case 3:
for (unsigned int i=0; i<monomials.size(); ++i)
monomials[i] = Polynomials::Monomial<double> (i);
break;
default:
Assert(false, ExcNotImplemented());
}
}
template <int dim>
void
PolynomialsBDM<dim>::compute (const Point<dim> &unit_point,
std::vector<Tensor<1,dim> > &values,
std::vector<Tensor<2,dim> > &grads,
std::vector<Tensor<3,dim> > &grad_grads,
std::vector<Tensor<4,dim> > &third_derivatives,
std::vector<Tensor<5,dim> > &fourth_derivatives) const
{
Assert(values.size()==n_pols || values.size()==0,
ExcDimensionMismatch(values.size(), n_pols));
Assert(grads.size()==n_pols|| grads.size()==0,
ExcDimensionMismatch(grads.size(), n_pols));
Assert(grad_grads.size()==n_pols|| grad_grads.size()==0,
ExcDimensionMismatch(grad_grads.size(), n_pols));
Assert(third_derivatives.size()==n_pols|| third_derivatives.size()==0,
ExcDimensionMismatch(third_derivatives.size(), n_pols));
Assert(fourth_derivatives.size()==n_pols|| fourth_derivatives.size()==0,
ExcDimensionMismatch(fourth_derivatives.size(), n_pols));
// third and fourth derivatives not implemented
(void)third_derivatives;
Assert(third_derivatives.size()==0,
ExcNotImplemented());
(void)fourth_derivatives;
Assert(fourth_derivatives.size()==0,
ExcNotImplemented());
const unsigned int n_sub = polynomial_space.n();
// guard access to the scratch
// arrays in the following block
// using a mutex to make sure they
// are not used by multiple threads
// at once
{
Threads::Mutex::ScopedLock lock(mutex);
p_values.resize((values.size() == 0) ? 0 : n_sub);
p_grads.resize((grads.size() == 0) ? 0 : n_sub);
p_grad_grads.resize((grad_grads.size() == 0) ? 0 : n_sub);
// Compute values of complete space
// and insert into tensors. Result
// will have first all polynomials
// in the x-component, then y and
// z.
polynomial_space.compute (unit_point, p_values, p_grads, p_grad_grads,
p_third_derivatives, p_fourth_derivatives);
std::fill(values.begin(), values.end(), Tensor<1,dim>());
for (unsigned int i=0; i<p_values.size(); ++i)
for (unsigned int j=0; j<dim; ++j)
values[i+j*n_sub][j] = p_values[i];
std::fill(grads.begin(), grads.end(), Tensor<2,dim>());
for (unsigned int i=0; i<p_grads.size(); ++i)
for (unsigned int j=0; j<dim; ++j)
grads[i+j*n_sub][j] = p_grads[i];
std::fill(grad_grads.begin(), grad_grads.end(), Tensor<3,dim>());
for (unsigned int i=0; i<p_grad_grads.size(); ++i)
for (unsigned int j=0; j<dim; ++j)
grad_grads[i+j*n_sub][j] = p_grad_grads[i];
}
// This is the first polynomial not
// covered by the P_k subspace
unsigned int start = dim*n_sub;
// Store values of auxiliary
// polynomials and their three
// derivatives
std::vector<std::vector<double> > monovali(dim, std::vector<double>(4));
std::vector<std::vector<double> > monovalk(dim, std::vector<double>(4));
if (dim == 2)
{
for (unsigned int d=0; d<dim; ++d)
monomials[0].value(unit_point(d), monovali[d]);
if (values.size() != 0)
{
values[start][0] = monovali[0][0];
values[start][1] = -unit_point(1) * monovali[0][1];
values[start+1][0] = unit_point(0) * monovali[1][1];
values[start+1][1] = -monovali[1][0];
}
if (grads.size() != 0)
{
grads[start][0][0] = monovali[0][1];
grads[start][0][1] = 0.;
grads[start][1][0] = -unit_point(1) * monovali[0][2];
grads[start][1][1] = -monovali[0][1];
grads[start+1][0][0] = monovali[1][1];
grads[start+1][0][1] = unit_point(0) * monovali[1][2];
grads[start+1][1][0] = 0.;
grads[start+1][1][1] = -monovali[1][1];
}
if (grad_grads.size() != 0)
{
grad_grads[start][0][0][0] = monovali[0][2];
grad_grads[start][0][0][1] = 0.;
grad_grads[start][0][1][0] = 0.;
grad_grads[start][0][1][1] = 0.;
grad_grads[start][1][0][0] = -unit_point(1) * monovali[0][3];
grad_grads[start][1][0][1] = -monovali[0][2];
grad_grads[start][1][1][0] = -monovali[0][2];
grad_grads[start][1][1][1] = 0.;
grad_grads[start+1][0][0][0] = 0;
grad_grads[start+1][0][0][1] = monovali[1][2];
grad_grads[start+1][0][1][0] = monovali[1][2];
grad_grads[start+1][0][1][1] = unit_point(0) * monovali[1][3];
grad_grads[start+1][1][0][0] = 0.;
grad_grads[start+1][1][0][1] = 0.;
grad_grads[start+1][1][1][0] = 0.;
grad_grads[start+1][1][1][1] = -monovali[1][2];
}
}
else // dim == 3
{
// The number of curls in each
// component. Note that the
// table in BrezziFortin91 has
// a typo, but the text has the
// right basis
// Note that the next basis
// function is always obtained
// from the previous by cyclic
// rotation of the coordinates
const unsigned int n_curls = monomials.size() - 1;
for (unsigned int i=0; i<n_curls; ++i, start+=dim)
{
for (unsigned int d=0; d<dim; ++d)
{
// p(t) = t^(i+1)
monomials[i+1].value(unit_point(d), monovali[d]);
// q(t) = t^(k-i)
monomials[degree()-i].value(unit_point(d), monovalk[d]);
}
if (values.size() != 0)
{
// x p'(y) q(z)
values[start][0] = unit_point(0) * monovali[1][1] * monovalk[2][0];
// - p(y) q(z)
values[start][1] = -monovali[1][0] * monovalk[2][0];
values[start][2] = 0.;
// y p'(z) q(x)
values[start+1][1] = unit_point(1) * monovali[2][1] * monovalk[0][0];
// - p(z) q(x)
values[start+1][2] = -monovali[2][0] * monovalk[0][0];
values[start+1][0] = 0.;
// z p'(x) q(y)
values[start+2][2] = unit_point(2) * monovali[0][1] * monovalk[1][0];
// -p(x) q(y)
values[start+2][0] = -monovali[0][0] * monovalk[1][0];
values[start+2][1] = 0.;
}
if (grads.size() != 0)
{
grads[start][0][0] = monovali[1][1] * monovalk[2][0];
grads[start][0][1] = unit_point(0) * monovali[1][2] * monovalk[2][0];
grads[start][0][2] = unit_point(0) * monovali[1][1] * monovalk[2][1];
grads[start][1][0] = 0.;
grads[start][1][1] = -monovali[1][1] * monovalk[2][0];
grads[start][1][2] = -monovali[1][0] * monovalk[2][1];
grads[start][2][0] = 0.;
grads[start][2][1] = 0.;
grads[start][2][2] = 0.;
grads[start+1][1][1] = monovali[2][1] * monovalk[0][0];
grads[start+1][1][2] = unit_point(1) * monovali[2][2] * monovalk[0][0];
grads[start+1][1][0] = unit_point(1) * monovali[2][1] * monovalk[0][1];
grads[start+1][2][1] = 0.;
grads[start+1][2][2] = -monovali[2][1] * monovalk[0][0];
grads[start+1][2][0] = -monovali[2][0] * monovalk[0][1];
grads[start+1][0][1] = 0.;
grads[start+1][0][2] = 0.;
grads[start+1][0][0] = 0.;
grads[start+2][2][2] = monovali[0][1] * monovalk[1][0];
grads[start+2][2][0] = unit_point(2) * monovali[0][2] * monovalk[1][0];
grads[start+2][2][1] = unit_point(2) * monovali[0][1] * monovalk[1][1];
grads[start+2][0][2] = 0.;
grads[start+2][0][0] = -monovali[0][1] * monovalk[1][0];
grads[start+2][0][1] = -monovali[0][0] * monovalk[1][1];
grads[start+2][1][2] = 0.;
grads[start+2][1][0] = 0.;
grads[start+2][1][1] = 0.;
}
if (grad_grads.size() != 0)
{
grad_grads[start][0][0][0] = 0.;
grad_grads[start][0][0][1] = monovali[1][2]*monovalk[2][0];
grad_grads[start][0][0][2] = monovali[1][1]*monovalk[2][1];
grad_grads[start][0][1][0] = monovali[1][2]*monovalk[2][0];
grad_grads[start][0][1][1] = unit_point(0)*monovali[1][3]*monovalk[2][0];
grad_grads[start][0][1][2] = unit_point(0)*monovali[1][2]*monovalk[2][1];
grad_grads[start][0][2][0] = monovali[1][1]*monovalk[2][1];
grad_grads[start][0][2][1] = unit_point(0)*monovali[1][2]*monovalk[2][1];
grad_grads[start][0][2][2] = unit_point(0)*monovali[1][1]*monovalk[2][2];
grad_grads[start][1][0][0] = 0.;
grad_grads[start][1][0][1] = 0.;
grad_grads[start][1][0][2] = 0.;
grad_grads[start][1][1][0] = 0.;
grad_grads[start][1][1][1] = -monovali[1][2]*monovalk[2][0];
grad_grads[start][1][1][2] = -monovali[1][1]*monovalk[2][1];
grad_grads[start][1][2][0] = 0.;
grad_grads[start][1][2][1] = -monovali[1][1]*monovalk[2][1];
grad_grads[start][1][2][2] = -monovali[1][0]*monovalk[2][2];
grad_grads[start][2][0][0] = 0.;
grad_grads[start][2][0][1] = 0.;
grad_grads[start][2][0][2] = 0.;
grad_grads[start][2][1][0] = 0.;
grad_grads[start][2][1][1] = 0.;
grad_grads[start][2][1][2] = 0.;
grad_grads[start][2][2][0] = 0.;
grad_grads[start][2][2][1] = 0.;
grad_grads[start][2][2][2] = 0.;
grad_grads[start+1][0][0][0] = 0.;
grad_grads[start+1][0][0][1] = 0.;
grad_grads[start+1][0][0][2] = 0.;
grad_grads[start+1][0][1][0] = 0.;
grad_grads[start+1][0][1][1] = 0.;
grad_grads[start+1][0][1][2] = 0.;
grad_grads[start+1][0][2][0] = 0.;
grad_grads[start+1][0][2][1] = 0.;
grad_grads[start+1][0][2][2] = 0.;
grad_grads[start+1][1][0][0] = unit_point(1)*monovali[2][1]*monovalk[0][2];
grad_grads[start+1][1][0][1] = monovali[2][1]*monovalk[0][1];
grad_grads[start+1][1][0][2] = unit_point(1)*monovali[2][2]*monovalk[0][1];
grad_grads[start+1][1][1][0] = monovalk[0][1]*monovali[2][1];
grad_grads[start+1][1][1][1] = 0.;
grad_grads[start+1][1][1][2] = monovalk[0][0]*monovali[2][2];
grad_grads[start+1][1][2][0] = unit_point(1)*monovalk[0][1]*monovali[2][2];
grad_grads[start+1][1][2][1] = monovalk[0][0]*monovali[2][2];
grad_grads[start+1][1][2][2] = unit_point(1)*monovalk[0][0]*monovali[2][3];
grad_grads[start+1][2][0][0] = -monovalk[0][2]*monovali[2][0];
grad_grads[start+1][2][0][1] = 0.;
grad_grads[start+1][2][0][2] = -monovalk[0][1]*monovali[2][1];
grad_grads[start+1][2][1][0] = 0.;
grad_grads[start+1][2][1][1] = 0.;
grad_grads[start+1][2][1][2] = 0.;
grad_grads[start+1][2][2][0] = -monovalk[0][1]*monovali[2][1];
grad_grads[start+1][2][2][1] = 0.;
grad_grads[start+1][2][2][2] = -monovalk[0][0]*monovali[2][2];
grad_grads[start+2][0][0][0] = -monovali[0][2]*monovalk[1][0];
grad_grads[start+2][0][0][1] = -monovali[0][1]*monovalk[1][1];
grad_grads[start+2][0][0][2] = 0.;
grad_grads[start+2][0][1][0] = -monovali[0][1]*monovalk[1][1];
grad_grads[start+2][0][1][1] = -monovali[0][0]*monovalk[1][2];
grad_grads[start+2][0][1][2] = 0.;
grad_grads[start+2][0][2][0] = 0.;
grad_grads[start+2][0][2][1] = 0.;
grad_grads[start+2][0][2][2] = 0.;
grad_grads[start+2][1][0][0] = 0.;
grad_grads[start+2][1][0][1] = 0.;
grad_grads[start+2][1][0][2] = 0.;
grad_grads[start+2][1][1][0] = 0.;
grad_grads[start+2][1][1][1] = 0.;
grad_grads[start+2][1][1][2] = 0.;
grad_grads[start+2][1][2][0] = 0.;
grad_grads[start+2][1][2][1] = 0.;
grad_grads[start+2][1][2][2] = 0.;
grad_grads[start+2][2][0][0] = unit_point(2)*monovali[0][3]*monovalk[1][0];
grad_grads[start+2][2][0][1] = unit_point(2)*monovali[0][2]*monovalk[1][1];
grad_grads[start+2][2][0][2] = monovali[0][2]*monovalk[1][0];
grad_grads[start+2][2][1][0] = unit_point(2)*monovali[0][2]*monovalk[1][1];
grad_grads[start+2][2][1][1] = unit_point(2)*monovali[0][1]*monovalk[1][2];
grad_grads[start+2][2][1][2] = monovali[0][1]*monovalk[1][1];
grad_grads[start+2][2][2][0] = monovali[0][2]*monovalk[1][0];
grad_grads[start+2][2][2][1] = monovali[0][1]*monovalk[1][1];
grad_grads[start+2][2][2][2] = 0.;
}
}
Assert(start == n_pols, ExcInternalError());
}
}
/*
template <int dim>
void
PolynomialsBDM<dim>::compute_node_matrix (Table<2,double>& A) const
{
std::vector<Polynomial<double> > moment_weight(2);
for (unsigned int i=0;i<moment_weight.size();++i)
moment_weight[i] = Monomial<double>(i);
QGauss<dim-1> qface(polynomial_space.degree()+1);
std::vector<Tensor<1,dim> > values(n());
std::vector<Tensor<2,dim> > grads;
std::vector<Tensor<3,dim> > grad_grads;
values.resize(n());
for (unsigned int face=0;face<2*dim;++face)
{
double orientation = 1.;
if ((face==0) || (face==3))
orientation = -1.;
for (unsigned int k=0;k<qface.size();++k)
{
const double w = qface.weight(k) * orientation;
const double x = qface.point(k)(0);
Point<dim> p;
switch (face)
{
case 2:
p(1) = 1.;
case 0:
p(0) = x;
break;
case 1:
p(0) = 1.;
case 3:
p(1) = x;
break;
}
// std::cerr << p
// << '\t' << moment_weight[0].value(x)
// << '\t' << moment_weight[1].value(x)
// ;
compute (p, values, grads, grad_grads);
for (unsigned int i=0;i<n();++i)
{
// std::cerr << '\t' << std::setw(6) << values[i][1-face%2];
// Integrate normal component.
// This is easy on the unit square
for (unsigned int j=0;j<moment_weight.size();++j)
A(moment_weight.size()*face+j,i)
+= w * values[i][1-face%2] * moment_weight[j].value(x);
}
// std::cerr << std::endl;
}
}
// Volume integrals are missing
//
// This degree is one larger
Assert (polynomial_space.degree() <= 2,
ExcNotImplemented());
}
*/
template <int dim>
unsigned int
PolynomialsBDM<dim>::compute_n_pols(unsigned int k)
{
if (dim == 1) return k+1;
if (dim == 2) return (k+1)*(k+2)+2;
if (dim == 3) return ((k+1)*(k+2)*(k+3))/2+3*(k+1);
Assert(false, ExcNotImplemented());
return 0;
}
template class PolynomialsBDM<1>;
template class PolynomialsBDM<2>;
template class PolynomialsBDM<3>;
DEAL_II_NAMESPACE_CLOSE
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