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operators.cpp
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operators.cpp
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#include <deal.II/base/conditional_ostream.h>
#include <deal.II/base/parameter_handler.h>
#include <deal.II/base/qprojector.h>
#include <deal.II/base/geometry_info.h>
#include <deal.II/grid/tria.h>
#include <deal.II/fe/fe_dgq.h>
#include <deal.II/fe/fe_dgp.h>
#include <deal.II/fe/fe_system.h>
#include <deal.II/fe/mapping_fe_field.h>
#include <deal.II/fe/mapping_q1_eulerian.h>
#include <deal.II/dofs/dof_handler.h>
#include <deal.II/hp/q_collection.h>
#include <deal.II/hp/mapping_collection.h>
#include <deal.II/hp/fe_values.h>
#include <deal.II/lac/vector.h>
#include <deal.II/lac/sparsity_pattern.h>
#include <deal.II/lac/trilinos_sparse_matrix.h>
#include <deal.II/lac/trilinos_vector.h>
#include <Epetra_RowMatrixTransposer.h>
#include <AztecOO.h>
#include "ADTypes.hpp"
#include <Sacado.hpp>
#include <CoDiPack/include/codi.hpp>
#include "operators.h"
namespace PHiLiP {
namespace OPERATOR {
//Constructor
template <int dim, int nstate, typename real>
OperatorBase<dim,nstate,real>::OperatorBase(
const Parameters::AllParameters *const parameters_input,
const unsigned int degree,
const unsigned int max_degree_input,
const unsigned int grid_degree_input)
: OperatorBase<dim,nstate,real>(parameters_input, degree, max_degree_input, grid_degree_input, this->create_collection_tuple(max_degree_input, parameters_input))
{ }
template <int dim, int nstate, typename real>
OperatorBase<dim,nstate,real>::OperatorBase(
const Parameters::AllParameters *const parameters_input,
const unsigned int /*degree*/,
const unsigned int max_degree_input,
const unsigned int grid_degree_input,
const MassiveCollectionTuple collection_tuple)
: all_parameters(parameters_input)
, max_degree(max_degree_input)
, max_grid_degree(grid_degree_input)
, fe_collection_basis(std::get<0>(collection_tuple))
, volume_quadrature_collection(std::get<1>(collection_tuple))
, face_quadrature_collection(std::get<2>(collection_tuple))
, oned_quadrature_collection(std::get<3>(collection_tuple))
, fe_collection_flux_basis(std::get<4>(collection_tuple))
, mpi_communicator(MPI_COMM_WORLD)
, pcout(std::cout, dealii::Utilities::MPI::this_mpi_process(mpi_communicator)==0)
{
pcout<<" Constructing Operators ..."<<std::endl;
//setup volume operators
allocate_volume_operators();
create_vol_basis_operators();
build_Mass_Matrix_operators();
build_Stiffness_Matrix_operators ();
get_higher_derivatives();
build_K_operators();
get_vol_projection_operators();
//setup surface operators
allocate_surface_operators();
create_surface_basis_operators();
get_surface_lifting_operators ();
//setup metric operators
allocate_metric_operators();
create_metric_basis_operators();
}
// Destructor
template <int dim, int nstate, typename real>
OperatorBase<dim,nstate,real>::~OperatorBase ()
{
pcout << "Destructing Operators..." << std::endl;
}
template <int dim, int nstate, typename real>
std::tuple<
dealii::hp::FECollection<dim>, // Solution FE basis functions
dealii::hp::QCollection<dim>, // Volume quadrature
dealii::hp::QCollection<dim-1>, // Face quadrature
dealii::hp::QCollection<1>, // 1D quadrature for strong form
dealii::hp::FECollection<dim> > // Flux Basis polynomials for strong form
OperatorBase<dim,nstate,real>::create_collection_tuple(const unsigned int max_degree, const Parameters::AllParameters *const parameters_input) const
{
dealii::hp::FECollection<dim> fe_coll;//basis functions collection
dealii::hp::QCollection<dim> volume_quad_coll;//volume flux nodes
dealii::hp::QCollection<dim-1> face_quad_coll;//facet flux nodes
dealii::hp::QCollection<1> oned_quad_coll;//1D flux nodes
dealii::hp::FECollection<dim> fe_coll_lagr;//flux basis collocated on flux nodes
// for p=0, we use a p=1 FE for collocation, since there's no p=0 quadrature for Gauss Lobatto
if (parameters_input->use_collocated_nodes==true)
{
int degree = 1;
const dealii::FE_DGQ<dim> fe_dg(degree);
const dealii::FESystem<dim,dim> fe_system(fe_dg, nstate);
fe_coll.push_back (fe_system);
dealii::Quadrature<1> oned_quad(degree+1);
dealii::Quadrature<dim> volume_quad(degree+1);
dealii::Quadrature<dim-1> face_quad(degree+1); //removed const
if (parameters_input->use_collocated_nodes) {
dealii::QGaussLobatto<1> oned_quad_Gauss_Lobatto (degree+1);
dealii::QGaussLobatto<dim> vol_quad_Gauss_Lobatto (degree+1);
oned_quad = oned_quad_Gauss_Lobatto;
volume_quad = vol_quad_Gauss_Lobatto;
if(dim == 1) {
dealii::QGauss<dim-1> face_quad_Gauss_Legendre (degree+1);
face_quad = face_quad_Gauss_Legendre;
} else {
dealii::QGaussLobatto<dim-1> face_quad_Gauss_Lobatto (degree+1);
face_quad = face_quad_Gauss_Lobatto;
}
} else {
dealii::QGauss<1> oned_quad_Gauss_Legendre (degree+1);
dealii::QGauss<dim> vol_quad_Gauss_Legendre (degree+1);
dealii::QGauss<dim-1> face_quad_Gauss_Legendre (degree+1);
oned_quad = oned_quad_Gauss_Legendre;
volume_quad = vol_quad_Gauss_Legendre;
face_quad = face_quad_Gauss_Legendre;
}
volume_quad_coll.push_back (volume_quad);
face_quad_coll.push_back (face_quad);
oned_quad_coll.push_back (oned_quad);
dealii::FE_DGQArbitraryNodes<dim,dim> lagrange_poly(oned_quad);
fe_coll_lagr.push_back (lagrange_poly);
}
int minimum_degree = (parameters_input->use_collocated_nodes==true) ? 1 : 0;
for (unsigned int degree=minimum_degree; degree<=max_degree; ++degree) {
// Solution FECollection
const dealii::FE_DGQ<dim> fe_dg(degree);
//const dealii::FE_DGQArbitraryNodes<dim,dim> fe_dg(dealii::QGauss<1>(degree+1));
//std::cout << degree << " fe_dg.tensor_degree " << fe_dg.tensor_degree() << " fe_dg.n_dofs_per_cell " << fe_dg.n_dofs_per_cell() << std::endl;
const dealii::FESystem<dim,dim> fe_system(fe_dg, nstate);
fe_coll.push_back (fe_system);
dealii::Quadrature<1> oned_quad(degree+1);
dealii::Quadrature<dim> volume_quad(degree+1);
dealii::Quadrature<dim-1> face_quad(degree+1); //removed const
if (parameters_input->use_collocated_nodes) {
dealii::QGaussLobatto<1> oned_quad_Gauss_Lobatto (degree+1);
dealii::QGaussLobatto<dim> vol_quad_Gauss_Lobatto (degree+1);
oned_quad = oned_quad_Gauss_Lobatto;
volume_quad = vol_quad_Gauss_Lobatto;
if(dim == 1)
{
dealii::QGauss<dim-1> face_quad_Gauss_Legendre (degree+1);
face_quad = face_quad_Gauss_Legendre;
}
else
{
dealii::QGaussLobatto<dim-1> face_quad_Gauss_Lobatto (degree+1);
face_quad = face_quad_Gauss_Lobatto;
}
} else {
const unsigned int overintegration = parameters_input->overintegration;
dealii::QGauss<1> oned_quad_Gauss_Legendre (degree+1+overintegration);
dealii::QGauss<dim> vol_quad_Gauss_Legendre (degree+1+overintegration);
dealii::QGauss<dim-1> face_quad_Gauss_Legendre (degree+1+overintegration);
oned_quad = oned_quad_Gauss_Legendre;
volume_quad = vol_quad_Gauss_Legendre;
face_quad = face_quad_Gauss_Legendre;
}
volume_quad_coll.push_back (volume_quad);
face_quad_coll.push_back (face_quad);
oned_quad_coll.push_back (oned_quad);
dealii::FE_DGQArbitraryNodes<dim,dim> lagrange_poly(oned_quad);
fe_coll_lagr.push_back (lagrange_poly);
}
return std::make_tuple(fe_coll, volume_quad_coll, face_quad_coll, oned_quad_coll, fe_coll_lagr);
}
template <int dim, int nstate, typename real>
double OperatorBase<dim,nstate,real>::compute_factorial(double n)
{
if ((n==0)||(n==1))
return 1;
else
return n*compute_factorial(n-1);
}
/*******************************************
*
* VOLUME OPERATORS FUNCTIONS
*
*
* *****************************************/
template <int dim, int nstate, typename real>
void OperatorBase<dim,nstate,real>::allocate_volume_operators ()
{
//basis functions evaluated at volume cubature (flux) nodes
basis_at_vol_cubature.resize(max_degree+1);
vol_integral_basis.resize(max_degree+1);
flux_basis_at_vol_cubature.resize(max_degree+1);
gradient_flux_basis.resize(max_degree+1);
modal_basis_differential_operator.resize(max_degree+1);
local_mass.resize(max_degree+1);
local_basis_stiffness.resize(max_degree+1);
local_flux_basis_stiffness.resize(max_degree+1);
vol_integral_gradient_basis.resize(max_degree+1);
derivative_p.resize(max_degree+1);
derivative_2p.resize(max_degree+1);
derivative_3p.resize(max_degree+1);
local_K_operator.resize(max_degree+1);
c_param_FR.resize(max_degree+1);
local_K_operator_aux.resize(max_degree+1);
k_param_FR.resize(max_degree+1);
vol_projection_operator.resize(max_degree+1);
vol_projection_operator_FR.resize(max_degree+1);
for(unsigned int idegree=0; idegree<=max_degree; idegree++){
unsigned int n_quad_pts = volume_quadrature_collection[idegree].size();
unsigned int n_dofs = fe_collection_basis[idegree].dofs_per_cell;
basis_at_vol_cubature[idegree].reinit(n_quad_pts, n_dofs);
vol_integral_basis[idegree].reinit(n_quad_pts, n_dofs);
modal_basis_differential_operator[idegree].resize(dim);
local_mass[idegree].reinit(n_dofs, n_dofs);
local_basis_stiffness[idegree].resize(dim);
derivative_p[idegree].resize(dim);
derivative_2p[idegree].resize(dim);
derivative_3p[idegree].reinit(n_dofs, n_dofs);
local_K_operator[idegree].reinit(n_dofs, n_dofs);
local_K_operator_aux[idegree].resize(dim);
vol_projection_operator[idegree].reinit(n_dofs, n_quad_pts);
vol_projection_operator_FR[idegree].reinit(n_dofs, n_quad_pts);
for(int idim=0; idim<dim; idim++){
modal_basis_differential_operator[idegree][idim].reinit(n_dofs, n_dofs);
local_basis_stiffness[idegree][idim].reinit(n_dofs, n_dofs);
derivative_p[idegree][idim].reinit(n_dofs, n_dofs);
derivative_2p[idegree][idim].reinit(n_dofs, n_dofs);
local_K_operator_aux[idegree][idim].reinit(n_dofs, n_dofs);
}
//flux basis allocator
unsigned int n_dofs_flux = fe_collection_flux_basis[idegree].dofs_per_cell;
flux_basis_at_vol_cubature[idegree].resize(nstate);
gradient_flux_basis[idegree].resize(nstate);
local_flux_basis_stiffness[idegree].resize(nstate);
vol_integral_gradient_basis[idegree].resize(nstate);
for(int istate=0; istate<nstate; istate++){
flux_basis_at_vol_cubature[idegree][istate].reinit(n_quad_pts, n_dofs_flux);
gradient_flux_basis[idegree][istate].resize(dim);
local_flux_basis_stiffness[idegree][istate].resize(dim);
vol_integral_gradient_basis[idegree][istate].resize(dim);
int shape_degree = (all_parameters->use_collocated_nodes==true && idegree==0) ? 1 : idegree;
const unsigned int n_shape_functions = pow(shape_degree+1,dim);
for(int idim=0; idim<dim; idim++){
gradient_flux_basis[idegree][istate][idim].reinit(n_quad_pts, n_dofs_flux);
local_flux_basis_stiffness[idegree][istate][idim].reinit(n_shape_functions, n_dofs_flux);
vol_integral_gradient_basis[idegree][istate][idim].reinit(n_quad_pts, n_shape_functions);
}
}
}
}
template <int dim, int nstate, typename real>
void OperatorBase<dim,nstate,real>::create_vol_basis_operators ()
{
for(unsigned int idegree=0; idegree<=max_degree; idegree++){
unsigned int n_quad_pts = volume_quadrature_collection[idegree].size();
unsigned int n_dofs = fe_collection_basis[idegree].dofs_per_cell;
unsigned int n_dofs_flux = fe_collection_flux_basis[idegree].dofs_per_cell;
for(unsigned int iquad=0; iquad<n_quad_pts; iquad++){
const dealii::Point<dim> qpoint = volume_quadrature_collection[idegree].point(iquad);
const std::vector<real> &quad_weights = volume_quadrature_collection[idegree].get_weights ();
for(unsigned int idof=0; idof<n_dofs; idof++){
const int istate = fe_collection_basis[idegree].system_to_component_index(idof).first;
basis_at_vol_cubature[idegree][iquad][idof] = fe_collection_basis[idegree].shape_value_component(idof,qpoint,istate);
vol_integral_basis[idegree][iquad][idof] = quad_weights[iquad] * basis_at_vol_cubature[idegree][iquad][idof];
}
for(int istate=0; istate<nstate; istate++){
for(unsigned int idof=0; idof<n_dofs_flux; idof++){
flux_basis_at_vol_cubature[idegree][istate][iquad][idof] = fe_collection_flux_basis[idegree].shape_value_component(idof,qpoint,0);
}
}
}
for(unsigned int iquad=0; iquad<n_quad_pts; iquad++){
const dealii::Point<dim> qpoint = volume_quadrature_collection[idegree].point(iquad);
for(int istate=0; istate<nstate; istate++){
for(unsigned int idof=0; idof<n_dofs_flux; idof++){
dealii::Tensor<1,dim,real> derivative;
derivative = fe_collection_flux_basis[idegree].shape_grad_component(idof, qpoint, 0);
for(int idim=0; idim<dim; idim++){
gradient_flux_basis[idegree][istate][idim][iquad][idof] = derivative[idim];
}
}
}
}
}
}
template <int dim, int nstate, typename real>
void OperatorBase<dim,nstate,real>::build_local_Mass_Matrix (
const std::vector<real> &quad_weights,
const unsigned int n_dofs_cell, const unsigned int n_quad_pts,
const int current_fe_index,
dealii::FullMatrix<real> &Mass_Matrix)
{
for (unsigned int itest=0; itest<n_dofs_cell; ++itest) {
const int istate_test = fe_collection_basis[current_fe_index].system_to_component_index(itest).first;
for (unsigned int itrial=itest; itrial<n_dofs_cell; ++itrial) {
const int istate_trial = fe_collection_basis[current_fe_index].system_to_component_index(itrial).first;
real value = 0.0;
for (unsigned int iquad=0; iquad<n_quad_pts; ++iquad) {
value +=
basis_at_vol_cubature[current_fe_index][iquad][itest]
* basis_at_vol_cubature[current_fe_index][iquad][itrial]
* quad_weights[iquad];//note that for mass matrix with metric Jacobian dependence pass JxW for quad_weights
}
Mass_Matrix[itrial][itest] = 0.0;
Mass_Matrix[itest][itrial] = 0.0;
if(istate_test==istate_trial) {
Mass_Matrix[itrial][itest] = value;
Mass_Matrix[itest][itrial] = value;
}
}
}
}
template <int dim, int nstate, typename real>
void OperatorBase<dim,nstate,real>::build_Mass_Matrix_operators ()
{
for(unsigned int idegree=0; idegree<=max_degree; idegree++){
unsigned int n_quad_pts = volume_quadrature_collection[idegree].size();
unsigned int n_dofs_cell = fe_collection_basis[idegree].dofs_per_cell;
const std::vector<real> &quad_weights = volume_quadrature_collection[idegree].get_weights ();
build_local_Mass_Matrix(quad_weights, n_dofs_cell, n_quad_pts, idegree, local_mass[idegree]);
}
}
template <int dim, int nstate, typename real>
void OperatorBase<dim,nstate,real>::build_Stiffness_Matrix_operators ()
{
for(unsigned int idegree=0; idegree<=max_degree; idegree++){
unsigned int n_quad_pts = volume_quadrature_collection[idegree].size();
unsigned int n_dofs = fe_collection_basis[idegree].dofs_per_cell;
unsigned int n_dofs_flux = fe_collection_flux_basis[idegree].dofs_per_cell;
const std::vector<real> &quad_weights = volume_quadrature_collection[idegree].get_weights ();
for(unsigned int itest=0; itest<n_dofs; itest++){
const int istate_test = fe_collection_basis[idegree].system_to_component_index(itest).first;
for(unsigned int idof=0; idof<n_dofs; idof++){
const int istate = fe_collection_basis[idegree].system_to_component_index(idof).first;
dealii::Tensor<1,dim,real> value;
for(unsigned int iquad=0; iquad<n_quad_pts; iquad++){
const dealii::Point<dim> qpoint = volume_quadrature_collection[idegree].point(iquad);
dealii::Tensor<1,dim,real> derivative;
derivative = fe_collection_basis[idegree].shape_grad_component(idof, qpoint, istate);
value += basis_at_vol_cubature[idegree][iquad][itest] * quad_weights[iquad] * derivative;
}
if(istate == istate_test){
for(int idim=0; idim<dim; idim++){
local_basis_stiffness[idegree][idim][itest][idof] = value[idim];
}
}
}
for(unsigned int idof=0; idof<n_dofs_flux; idof++){
// const int istate = fe_collection_flux_basis[idegree].system_to_component_index(idof).first;
dealii::Tensor<1,dim,real> value;
for(unsigned int iquad=0; iquad<n_quad_pts; iquad++){
const dealii::Point<dim> qpoint = volume_quadrature_collection[idegree].point(iquad);
dealii::Tensor<1,dim,real> derivative;
derivative = fe_collection_flux_basis[idegree].shape_grad_component(idof, qpoint, 0);
value += basis_at_vol_cubature[idegree][iquad][itest] * quad_weights[iquad] * derivative;
}
// if(istate == istate_test){
const int test_shape = fe_collection_basis[idegree].system_to_component_index(itest).second;
for(int idim=0; idim<dim; idim++){
local_flux_basis_stiffness[idegree][istate_test][idim][test_shape][idof] = value[idim];
}
// }
}
const int ishape_test = fe_collection_basis[idegree].system_to_component_index(itest).second;
for(unsigned int iquad=0; iquad<n_quad_pts; iquad++){
const dealii::Point<dim> qpoint = volume_quadrature_collection[idegree].point(iquad);
dealii::Tensor<1,dim,real> derivative;
derivative = fe_collection_basis[idegree].shape_grad_component(itest, qpoint, istate_test);
for(int idim=0; idim<dim; idim++){
vol_integral_gradient_basis[idegree][istate_test][idim][iquad][ishape_test] = derivative[idim] * quad_weights[iquad];
}
}
}
// for(int idim=0; idim<dim; idim++){
// vol_integral_basis[idegree].Tmmult(local_flux_basis_stiffness[idegree][idim], gradient_flux_basis[idegree][idim]);
// }
for(int idim=0; idim<dim; idim++){
dealii::FullMatrix<real> inv_mass(n_dofs);
inv_mass.invert(local_mass[idegree]);
inv_mass.mmult(modal_basis_differential_operator[idegree][idim],local_basis_stiffness[idegree][idim]);
}
}
}
template <int dim, int nstate, typename real>
void OperatorBase<dim,nstate,real>::get_higher_derivatives ()
{
for(unsigned int curr_cell_degree=0;curr_cell_degree<=max_degree; curr_cell_degree++){
// unsigned int degree_index = curr_cell_degree - 1;
unsigned int degree_index = curr_cell_degree;
unsigned int n_dofs_cell = fe_collection_basis[degree_index].dofs_per_cell;
//write each deriv p to identity
for(int idim=0; idim<dim; idim++){
for(unsigned int idof=0; idof<n_dofs_cell; idof++){
for(unsigned int idof2=0; idof2<n_dofs_cell; idof2++){
if(idof == idof2){
derivative_p[degree_index][idim][idof][idof2] = 1.0;//set it equal to identity
}
}
}
}
for(int idim=0; idim<dim; idim++){
for(unsigned int idegree=0; idegree< curr_cell_degree; idegree++){
dealii::FullMatrix<real> derivative_p_temp(n_dofs_cell, n_dofs_cell);
derivative_p_temp.add(1, derivative_p[degree_index][idim]);
modal_basis_differential_operator[degree_index][idim].mmult(derivative_p[degree_index][idim], derivative_p_temp);
}
#if 0
//method above loses accuracy for higher poly
if(curr_cell_degree==3){
const unsigned int n_quad_pts = volume_quadrature_collection[curr_cell_degree].size();
dealii::FullMatrix<real> temp(n_quad_pts, n_dofs_cell);
for(unsigned int idof=0; idof<n_dofs_cell; idof++){
for(unsigned int iquad=0; iquad<n_quad_pts; iquad++){
const dealii::Point<dim> qpoint = volume_quadrature_collection[curr_cell_degree].point(iquad);
const int istate = fe_collection_basis[curr_cell_degree].system_to_component_index(idof).first;
dealii::Tensor<3, dim, real> deriv_3 = fe_collection_basis[curr_cell_degree].shape_3rd_derivative_component(idof, qpoint, istate);
temp[iquad][idof] = deriv_3[idim][idim][idim];
}
}
dealii::FullMatrix<real> project(n_dofs_cell,n_quad_pts);
compute_local_vol_projection_operator(curr_cell_degree,n_dofs_cell,local_mass[curr_cell_degree],project);
}
if(curr_cell_degree >= 4){
const unsigned int n_quad_pts = volume_quadrature_collection[curr_cell_degree].size();
dealii::FullMatrix<real> temp(n_quad_pts, n_dofs_cell);
for(unsigned int idof=0; idof<n_dofs_cell; idof++){
for(unsigned int iquad=0; iquad<n_quad_pts; iquad++){
const dealii::Point<dim> qpoint = volume_quadrature_collection[curr_cell_degree].point(iquad);
const int istate = fe_collection_basis[curr_cell_degree].system_to_component_index(idof).first;
dealii::Tensor<4, dim, real> deriv_4 = fe_collection_basis[curr_cell_degree].shape_4th_derivative_component(idof,qpoint, istate);
temp[iquad][idof] = deriv_4[idim][idim][idim][idim];
}
}
dealii::FullMatrix<real> project(n_dofs_cell,n_quad_pts);
compute_local_vol_projection_operator(curr_cell_degree,n_dofs_cell,local_mass[curr_cell_degree],project);
project.mmult(derivative_p[degree_index][idim], temp);
for(unsigned int idegree=4; idegree< curr_cell_degree; idegree++){
dealii::FullMatrix<real> derivative_p_temp(n_dofs_cell, n_dofs_cell);
derivative_p_temp.add(1, derivative_p[degree_index][idim]);
modal_basis_differential_operator[degree_index][idim].mmult(derivative_p[degree_index][idim], derivative_p_temp);
}
}
#endif
}
if(dim == 2){
derivative_p[degree_index][0].mmult(derivative_2p[degree_index][0],derivative_p[degree_index][1]);
}
if(dim==3){
derivative_p[degree_index][0].mmult(derivative_2p[degree_index][0],derivative_p[degree_index][1]);
derivative_p[degree_index][0].mmult(derivative_2p[degree_index][1],derivative_p[degree_index][2]);
derivative_p[degree_index][1].mmult(derivative_2p[degree_index][2],derivative_p[degree_index][2]);
derivative_p[degree_index][0].mmult(derivative_3p[degree_index],derivative_2p[degree_index][2]);
}
}
}
template <int dim, int nstate, typename real>
void OperatorBase<dim,nstate,real>::get_FR_correction_parameter (
const unsigned int curr_cell_degree,
real &c, real &k)
{
using FR_enum = Parameters::AllParameters::Flux_Reconstruction;
using FR_Aux_enum = Parameters::AllParameters::Flux_Reconstruction_Aux;
FR_enum c_input = this->all_parameters->flux_reconstruction_type;
FR_Aux_enum k_input = this->all_parameters->flux_reconstruction_aux_type;
if(c_input == FR_enum::cHU || c_input == FR_enum::cHULumped){
const double pfact = compute_factorial(curr_cell_degree);
const double pfact2 = compute_factorial(2.0 * curr_cell_degree);
// double cp = 1.0/(pow(2.0,curr_cell_degree)) * pfact2/(pow(pfact,2));
double cp = pfact2/(pow(pfact,2));//since ref element [0,1]
//c = 2.0 * (curr_cell_degree+1)/( curr_cell_degree*pow((2.0*curr_cell_degree+1.0)*(pow(pfact*cp,2)),dim));
c = 2.0 * (curr_cell_degree+1)/( curr_cell_degree*((2.0*curr_cell_degree+1.0)*(pow(pfact*cp,2))));
c/=2.0;//since orthonormal
}
else if(c_input == FR_enum::cSD){
const double pfact = compute_factorial(curr_cell_degree);
const double pfact2 = compute_factorial(2.0 * curr_cell_degree);
// double cp = 1.0/(pow(2.0,curr_cell_degree)) * pfact2/(pow(pfact,2));
double cp = pfact2/(pow(pfact,2));
// c = 2.0 * (curr_cell_degree)/( (curr_cell_degree+1.0)*pow((2.0*curr_cell_degree+1.0)*(pow(pfact*cp,2)),dim));
c = 2.0 * (curr_cell_degree)/( (curr_cell_degree+1.0)*((2.0*curr_cell_degree+1.0)*(pow(pfact*cp,2))));
c/=2.0;//since orthonormal
}
else if(c_input == FR_enum::cNegative){
const double pfact = compute_factorial(curr_cell_degree);
const double pfact2 = compute_factorial(2.0 * curr_cell_degree);
// double cp = 1.0/(pow(2,curr_cell_degree)) * pfact2/(pow(pfact,2));
double cp = pfact2/(pow(pfact,2));
// c = - 2.0 / ( pow((2.0*curr_cell_degree+1.0)*(pow(pfact*cp,2)),dim));
c = - 2.0 / ( pow((2.0*curr_cell_degree+1.0)*(pow(pfact*cp,2)),1.0));
c/=2.0;//since orthonormal
}
else if(c_input == FR_enum::cNegative2){
const double pfact = compute_factorial(curr_cell_degree);
const double pfact2 = compute_factorial(2.0 * curr_cell_degree);
// double cp = 1.0/(pow(2,curr_cell_degree)) * pfact2/(pow(pfact,2));
double cp = pfact2/(pow(pfact,2));
// c = - 2.0 / ( pow((2.0*curr_cell_degree+1.0)*(pow(pfact*cp,2)),dim));
c = - 2.0 / ( pow((2.0*curr_cell_degree+1.0)*(pow(pfact*cp,2)),1.0));
c/=2.0;//since orthonormal
c/=2.0;//since cneg/2
}
else if(c_input == FR_enum::cDG){
c = 0.0;
}
else if(c_input == FR_enum::c10Thousand){
c = 10000.0;
// c = 10.0;
}
else if(c_input == FR_enum::cPlus){
// const double pfact = compute_factorial(curr_cell_degree);
// const double pfact2 = compute_factorial(2.0 * curr_cell_degree);
// double cp = pfact2/(pow(pfact,2));
if(curr_cell_degree == 2){
c = 0.186;
// c = 0.173;//RK33
}
if(curr_cell_degree == 3)
c = 3.67e-3;
if(curr_cell_degree == 4){
c = 4.79e-5;
// c = 4.92e-5;//RK33
}
if(curr_cell_degree == 5)
c = 4.24e-7;
// c=0.01;
c/=2.0;//since orthonormal
c/=pow(pow(2.0,curr_cell_degree),2);//since ref elem [0,1]
// c /= pow((2.0*curr_cell_degree+1.0)*(pow(pfact*cp,2)),dim -1.0);//for multiple dim tensor product
// c *= pow((2.0*curr_cell_degree+1.0)*(pow(pfact*cp,2)),dim -1.0);//for multiple dim tensor product
// c= 100000000.0;
}
else if(c_input == FR_enum::cPlus1D){
if(curr_cell_degree == 2){
c = 0.186;
// c = 0.173;//RK33
}
if(curr_cell_degree == 3)
c = 3.67e-3;
if(curr_cell_degree == 4){
c = 4.79e-5;
// c = 4.92e-5;//RK33
}
if(curr_cell_degree == 5)
c = 4.24e-7;
c/=2.0;//since orthonormal
c/=pow(pow(2.0,curr_cell_degree),2);//since ref elem [0,1]
// c+=0.001;
// c+=0.01;
}
if(k_input == FR_Aux_enum::kHU){
const double pfact = compute_factorial(curr_cell_degree);
const double pfact2 = compute_factorial(2.0 * curr_cell_degree);
// double cp = 1.0/(pow(2.0,curr_cell_degree)) * pfact2/(pow(pfact,2));
double cp = pfact2/(pow(pfact,2));
// k = 2.0 * (curr_cell_degree+1.0)/( curr_cell_degree*pow((2.0*curr_cell_degree+1.0)*(pow(pfact*cp,2)),dim));
k = 2.0 * (curr_cell_degree+1.0)/( curr_cell_degree*pow((2.0*curr_cell_degree+1.0)*(pow(pfact*cp,2)),1.0));
k/=2.0;//since orthonormal
}
else if(k_input == FR_Aux_enum::kSD){
const double pfact = compute_factorial(curr_cell_degree);
const double pfact2 = compute_factorial(2.0 * curr_cell_degree);
// double cp = 1.0/(pow(2.0,curr_cell_degree)) * pfact2/(pow(pfact,2));
double cp = pfact2/(pow(pfact,2));
// k = 2.0 * (curr_cell_degree)/( (curr_cell_degree+1.0)*pow((2.0*curr_cell_degree+1.0)*(pow(pfact*cp,2)),dim));
k = 2.0 * (curr_cell_degree)/( (curr_cell_degree+1.0)*pow((2.0*curr_cell_degree+1.0)*(pow(pfact*cp,2)),1.0));
k/=2.0;//since orthonormal
}
else if(k_input == FR_Aux_enum::kNegative){
const double pfact = compute_factorial(curr_cell_degree);
const double pfact2 = compute_factorial(2.0 * curr_cell_degree);
// double cp = 1.0/(pow(2.0,curr_cell_degree)) * pfact2/(pow(pfact,2));
double cp = pfact2/(pow(pfact,2));
// k = - 2.0 / ( pow((2.0*curr_cell_degree+1.0)*(pow(pfact*cp,2)),dim));
k = - 2.0 / ( pow((2.0*curr_cell_degree+1.0)*(pow(pfact*cp,2)),1.0));
k/=2.0;//since orthonormal
}
else if(k_input == FR_Aux_enum::kNegative2){
const double pfact = compute_factorial(curr_cell_degree);
const double pfact2 = compute_factorial(2.0 * curr_cell_degree);
// double cp = 1.0/(pow(2.0,curr_cell_degree)) * pfact2/(pow(pfact,2));
double cp = pfact2/(pow(pfact,2));
// k = - 2.0 / ( pow((2.0*curr_cell_degree+1.0)*(pow(pfact*cp,2)),dim));
k = - 2.0 / ( pow((2.0*curr_cell_degree+1.0)*(pow(pfact*cp,2)),1.0));
k/=2.0;//since orthonormal
k/=2.0;
}
else if(k_input == FR_Aux_enum::kDG){
k = 0.0;
}
else if(k_input == FR_Aux_enum::k10Thousand){
k = 10000.0;
}
else if(k_input == FR_Aux_enum::kPlus){
// const double pfact = compute_factorial(curr_cell_degree);
// const double pfact2 = compute_factorial(2.0 * curr_cell_degree);
// double cp = pfact2/(pow(pfact,2));
if(curr_cell_degree == 2)
{
k = 0.186;
// k = 0.173;//RK33
}
if(curr_cell_degree == 3)
{
k = 3.67e-3;
}
if(curr_cell_degree == 4){
k = 4.79e-5;
// k = 4.92e-5;//RK33
}
if(curr_cell_degree == 5)
k = 4.24e-7;
k/=2.0;//since orthonormal
k/=pow(pow(2.0,curr_cell_degree),2);//since ref elem [0,1]
// k /= pow((2.0*curr_cell_degree+1.0)*(pow(pfact*cp,2)),dim -1.0);//for multiple dim tensor product
}
}
template <int dim, int nstate, typename real>
void OperatorBase<dim, nstate, real>::build_local_K_operator(
const dealii::FullMatrix<real> &local_Mass_Matrix,
const unsigned int n_dofs_cell, const unsigned int degree_index,
dealii::FullMatrix<real> &K_operator)
{
real c = 0.0;
//get the K operator
c = c_param_FR[degree_index];
if(dim == 1){
dealii::FullMatrix<real> derivative_p_temp(n_dofs_cell, n_dofs_cell);
derivative_p_temp.add(c, derivative_p[degree_index][0]);
dealii::FullMatrix<real> K_operator_temp(n_dofs_cell);
derivative_p_temp.Tmmult(K_operator_temp, local_Mass_Matrix);
K_operator_temp.mmult(K_operator, derivative_p[degree_index][0]);
}
if(dim == 2){
for(int idim=0; idim<dim; idim++){
dealii::FullMatrix<real> derivative_p_temp(n_dofs_cell, n_dofs_cell);
derivative_p_temp.add(c, derivative_p[degree_index][idim]);
dealii::FullMatrix<real> K_operator_temp(n_dofs_cell);
derivative_p_temp.Tmmult(K_operator_temp, local_Mass_Matrix);
K_operator_temp.mmult(K_operator, derivative_p[degree_index][idim], true);
}
double c_2 = pow(c,2.0);
dealii::FullMatrix<real> derivative_p_temp(n_dofs_cell, n_dofs_cell);
derivative_p_temp.add(c_2, derivative_2p[degree_index][0]);
dealii::FullMatrix<real> K_operator_temp(n_dofs_cell);
derivative_p_temp.Tmmult(K_operator_temp, local_Mass_Matrix);
K_operator_temp.mmult(K_operator, derivative_2p[degree_index][0], true);
}
if(dim == 3){
for(int idim=0; idim<dim; idim++){
dealii::FullMatrix<real> derivative_p_temp(n_dofs_cell, n_dofs_cell);
derivative_p_temp.add(c, derivative_p[degree_index][idim]);
dealii::FullMatrix<real> K_operator_temp(n_dofs_cell);
derivative_p_temp.Tmmult(K_operator_temp, local_Mass_Matrix);
K_operator_temp.mmult(K_operator, derivative_p[degree_index][idim], true);
}
for(int idim=0; idim<dim; idim++){
double c_2 = pow(c,2.0);
dealii::FullMatrix<real> derivative_p_temp(n_dofs_cell, n_dofs_cell);
derivative_p_temp.add(c_2, derivative_2p[degree_index][idim]);
dealii::FullMatrix<real> K_operator_temp(n_dofs_cell);
derivative_p_temp.Tmmult(K_operator_temp, local_Mass_Matrix);
K_operator_temp.mmult(K_operator, derivative_2p[degree_index][idim], true);
}
double c_3 = pow(c,3.0);
dealii::FullMatrix<real> derivative_p_temp(n_dofs_cell, n_dofs_cell);
derivative_p_temp.add(c_3, derivative_3p[degree_index]);
dealii::FullMatrix<real> K_operator_temp(n_dofs_cell);
derivative_p_temp.Tmmult(K_operator_temp, local_Mass_Matrix);
K_operator_temp.mmult(K_operator, derivative_3p[degree_index], true);
}
}
template <int dim, int nstate, typename real>
void OperatorBase<dim, nstate, real>::build_local_K_operator_AUX(
const dealii::FullMatrix<real> &local_Mass_Matrix,
const unsigned int n_dofs_cell, const unsigned int degree_index,
std::vector<dealii::FullMatrix<real>> &K_operator_aux)
{
real k = 0.0;
//get the K AUX operator
k = k_param_FR[degree_index];
for(int idim=0; idim<dim; idim++){
dealii::FullMatrix<real> derivative_p_temp2(n_dofs_cell, n_dofs_cell);
dealii::FullMatrix<real> K_operator_temp(n_dofs_cell);
derivative_p_temp2.add(k,derivative_p[degree_index][idim]);
derivative_p_temp2.Tmmult(K_operator_temp, local_Mass_Matrix);
K_operator_temp.mmult(K_operator_aux[idim], derivative_p[degree_index][idim]);
}
}
template <int dim, int nstate, typename real>
void OperatorBase<dim,nstate,real>::build_K_operators ()
{
for(unsigned int degree_index=0; degree_index<=max_degree; degree_index++){
unsigned int n_dofs_cell = fe_collection_basis[degree_index].dofs_per_cell;
unsigned int curr_cell_degree = degree_index;
get_FR_correction_parameter(curr_cell_degree, c_param_FR[degree_index], k_param_FR[degree_index]);
build_local_K_operator(local_mass[degree_index], n_dofs_cell, degree_index, local_K_operator[degree_index]);
build_local_K_operator_AUX(local_mass[degree_index], n_dofs_cell, degree_index, local_K_operator_aux[degree_index]);
#if 0
pcout<<"K operator "<<std::endl;
for(unsigned int idof=0; idof<n_dofs_cell; idof++){
for(unsigned int idof2=0; idof2<n_dofs_cell; idof2++){
pcout<<local_K_operator[degree_index][idof][idof2]<<" ";
}
pcout<<std::endl;
}
#endif
}
}
template <int dim, int nstate, typename real>
void OperatorBase<dim, nstate, real>::compute_local_vol_projection_operator(
const unsigned int degree_index,
const unsigned int n_dofs_cell,
const dealii::FullMatrix<real> &norm_matrix,
dealii::FullMatrix<real> &volume_projection)
{
dealii::FullMatrix<real> norm_inv(n_dofs_cell);
norm_inv.invert(norm_matrix);
norm_inv.mTmult(volume_projection, vol_integral_basis[degree_index]);
}
template <int dim, int nstate, typename real>
void OperatorBase<dim,nstate,real>::get_vol_projection_operators ()
{
for(unsigned int degree_index=0; degree_index<=max_degree; degree_index++){
unsigned int n_dofs = fe_collection_basis[degree_index].dofs_per_cell;
compute_local_vol_projection_operator(degree_index, n_dofs, local_mass[degree_index], vol_projection_operator[degree_index]);
dealii::FullMatrix<real> M_plus_K(n_dofs);
M_plus_K.add(1.0, local_mass[degree_index], 1.0, local_K_operator[degree_index]);
compute_local_vol_projection_operator(degree_index, n_dofs, M_plus_K, vol_projection_operator_FR[degree_index]);
}
}
/*******************************************
*
* SURFACE OPERATORS FUNCTIONS
*
*
* *****************************************/
template <int dim, int nstate, typename real>
void OperatorBase<dim,nstate,real>::allocate_surface_operators ()
{
unsigned int n_faces = dealii::GeometryInfo<dim>::faces_per_cell;
basis_at_facet_cubature.resize(max_degree+1);
flux_basis_at_facet_cubature.resize(max_degree+1);
face_integral_basis.resize(max_degree+1);
lifting_operator.resize(max_degree+1);
lifting_operator_FR.resize(max_degree+1);
for(unsigned int idegree=0; idegree<=max_degree; idegree++){
unsigned int n_quad_face_pts = face_quadrature_collection[idegree].size();
unsigned int n_dofs = fe_collection_basis[idegree].dofs_per_cell;
unsigned int n_dofs_flux = fe_collection_flux_basis[idegree].dofs_per_cell;
basis_at_facet_cubature[idegree].resize(n_faces);
face_integral_basis[idegree].resize(n_faces);
lifting_operator[idegree].resize(n_faces);
lifting_operator_FR[idegree].resize(n_faces);
for(unsigned int iface=0; iface<n_faces; iface++){
basis_at_facet_cubature[idegree][iface].reinit(n_quad_face_pts, n_dofs);
face_integral_basis[idegree][iface].resize(dim);
lifting_operator[idegree][iface].resize(dim);
lifting_operator_FR[idegree][iface].resize(dim);
for(int idim=0; idim<dim; idim++){
face_integral_basis[idegree][iface][idim].reinit(n_quad_face_pts, n_dofs);
lifting_operator[idegree][iface][idim].reinit(n_dofs, n_quad_face_pts);
lifting_operator_FR[idegree][iface][idim].reinit(n_dofs, n_quad_face_pts);
}
}
//for flux basis by nstate
flux_basis_at_facet_cubature[idegree].resize(nstate);
// int shape_degree = (all_parameters->use_collocated_nodes==true && idegree==0) ? 1 : idegree;
// const unsigned int n_shape_functions = pow(shape_degree+1,dim);
for(int istate=0; istate<nstate; istate++){
flux_basis_at_facet_cubature[idegree][istate].resize(n_faces);
for(unsigned int iface=0; iface<n_faces; iface++){
flux_basis_at_facet_cubature[idegree][istate][iface].reinit(n_quad_face_pts, n_dofs_flux);
//flux_basis_at_facet_cubature[idegree][istate][iface].reinit(n_quad_face_pts, n_shape_functions);
}
}
}
}
template <int dim, int nstate, typename real>
void OperatorBase<dim,nstate,real>::create_surface_basis_operators ()
{
unsigned int n_faces = dealii::GeometryInfo<dim>::faces_per_cell;
for(unsigned int idegree=0; idegree<=max_degree; idegree++){
unsigned int n_dofs = fe_collection_basis[idegree].dofs_per_cell;
unsigned int n_dofs_flux = fe_collection_flux_basis[idegree].dofs_per_cell;
//int shape_degree = (all_parameters->use_collocated_nodes==true && idegree==0) ? 1 : idegree;
//const unsigned int n_shape_functions = pow(shape_degree+1,dim);
unsigned int n_quad_face_pts = face_quadrature_collection[idegree].size();
const std::vector<real> &quad_weights = face_quadrature_collection[idegree].get_weights ();
for(unsigned int iface=0; iface<n_faces; iface++){
const dealii::Quadrature<dim> quadrature = dealii::QProjector<dim>::project_to_face(dealii::ReferenceCell::get_hypercube(dim),
face_quadrature_collection[idegree],
iface);
const dealii::Tensor<1,dim,real> unit_normal_int = dealii::GeometryInfo<dim>::unit_normal_vector[iface];
for(unsigned int iquad=0; iquad<n_quad_face_pts; iquad++){
for(unsigned int idof=0; idof<n_dofs; idof++){
const int istate = fe_collection_basis[idegree].system_to_component_index(idof).first;
basis_at_facet_cubature[idegree][iface][iquad][idof] = fe_collection_basis[idegree].shape_value_component(idof,quadrature.point(iquad),istate);
for(int idim=0; idim<dim; idim++){
face_integral_basis[idegree][iface][idim][iquad][idof] =
basis_at_facet_cubature[idegree][iface][iquad][idof]
* unit_normal_int[idim]
* quad_weights[iquad];
}
}
for(int istate=0; istate<nstate; istate++){
for(unsigned int idof=0; idof<n_dofs_flux; idof++){
flux_basis_at_facet_cubature[idegree][istate][iface][iquad][idof] = fe_collection_flux_basis[idegree].shape_value_component(idof,quadrature.point(iquad),0);
}
}
}
}
}
}
template <int dim, int nstate, typename real>
void OperatorBase<dim,nstate,real>::build_local_surface_lifting_operator (
const unsigned int degree_index,
const unsigned int n_dofs_cell,
const unsigned int face_number,
const dealii::FullMatrix<real> &norm_matrix,
std::vector<dealii::FullMatrix<real>> &lifting)
{
dealii::FullMatrix<real> norm_inv(n_dofs_cell);
norm_inv.invert(norm_matrix);
for(int idim=0; idim<dim; idim++){
norm_matrix.mTmult(lifting[idim], face_integral_basis[degree_index][face_number][idim]);
}
}
template <int dim, int nstate, typename real>
void OperatorBase<dim,nstate,real>::get_surface_lifting_operators ()
{
unsigned int n_faces = dealii::GeometryInfo<dim>::faces_per_cell;
for(unsigned int degree_index=0; degree_index<=max_degree; degree_index++){
unsigned int n_dofs = fe_collection_basis[degree_index].dofs_per_cell;
#if 0
pcout<<"K operator "<<std::endl;
for(unsigned int idof=0; idof<n_dofs; idof++){
for(unsigned int idof2=0; idof2<n_dofs; idof2++){
pcout<<local_K_operator[degree_index][idof][idof2]<<" ";
}
pcout<<std::endl;
}
#endif
for(unsigned int iface=0; iface<n_faces; iface++){
build_local_surface_lifting_operator(degree_index, n_dofs, iface, local_mass[degree_index], lifting_operator[degree_index][iface]);
dealii::FullMatrix<real> M_plus_K(n_dofs);
M_plus_K.add(1.0, local_mass[degree_index], 1.0, local_K_operator[degree_index]);
build_local_surface_lifting_operator(degree_index, n_dofs, iface, M_plus_K, lifting_operator_FR[degree_index][iface]);
}
}
}
/*********************************************************************
*
* METRIC OPERATOR FUNCTIONS
*
* ******************************************************/
template <int dim, int nstate, typename real>
void OperatorBase<dim,nstate,real>::allocate_metric_operators ()
{
unsigned int n_faces = dealii::GeometryInfo<dim>::faces_per_cell;
mapping_shape_functions_grid_nodes.resize(max_grid_degree+1);
gradient_mapping_shape_functions_grid_nodes.resize(max_grid_degree+1);
mapping_shape_functions_vol_flux_nodes.resize(max_grid_degree+1);
mapping_shape_functions_face_flux_nodes.resize(max_grid_degree+1);
gradient_mapping_shape_functions_vol_flux_nodes.resize(max_grid_degree+1);
gradient_mapping_shape_functions_face_flux_nodes.resize(max_grid_degree+1);
for(unsigned int idegree=0; idegree<=max_grid_degree; idegree++){
// unsigned int n_dofs = dim * pow(idegree+1,dim);
unsigned int n_dofs = pow(idegree+1,dim);
mapping_shape_functions_grid_nodes[idegree].reinit(n_dofs, n_dofs);
gradient_mapping_shape_functions_grid_nodes[idegree].resize(dim);
for(int idim=0; idim<dim; idim++){
gradient_mapping_shape_functions_grid_nodes[idegree][idim].reinit(n_dofs, n_dofs);
}
#if 0
unsigned int n_face_quad_pts = pow(idegree+1,dim-1);
for(unsigned int iface=0; iface<n_faces; iface++){
mapping_shape_functions_face_flux_nodes[idegree][iface].reinit(n_face_quad_pts, n_dofs);
gradient_mapping_shape_functions_face_flux_nodes[idegree][iface].resize(dim);
for(int idim=0; idim<dim; idim++){
gradient_mapping_shape_functions_face_flux_nodes[idegree][iface][idim].reinit(n_face_quad_pts, n_dofs);
}
}
#endif
//initialize flux sets
mapping_shape_functions_vol_flux_nodes[idegree].resize(max_degree+1);
mapping_shape_functions_face_flux_nodes[idegree].resize(max_degree+1);
gradient_mapping_shape_functions_vol_flux_nodes[idegree].resize(max_degree+1);
gradient_mapping_shape_functions_face_flux_nodes[idegree].resize(max_degree+1);
for(unsigned int iflux_degree=0; iflux_degree<=max_degree; iflux_degree++){
const unsigned int n_quad_pts = volume_quadrature_collection[iflux_degree].size();
mapping_shape_functions_vol_flux_nodes[idegree][iflux_degree].reinit(n_quad_pts, n_dofs);
mapping_shape_functions_face_flux_nodes[idegree][iflux_degree].resize(n_faces);
gradient_mapping_shape_functions_vol_flux_nodes[idegree][iflux_degree].resize(dim);
gradient_mapping_shape_functions_face_flux_nodes[idegree][iflux_degree].resize(n_faces);
for(int idim=0; idim<dim; idim++){
gradient_mapping_shape_functions_vol_flux_nodes[idegree][iflux_degree][idim].reinit(n_quad_pts, n_dofs);
}
const unsigned int n_face_quad_pts = face_quadrature_collection[iflux_degree].size();
for(unsigned int iface=0; iface<n_faces; iface++){
mapping_shape_functions_face_flux_nodes[idegree][iflux_degree][iface].reinit(n_face_quad_pts, n_dofs);
gradient_mapping_shape_functions_face_flux_nodes[idegree][iflux_degree][iface].resize(dim);
for(int idim=0; idim<dim; idim++){
gradient_mapping_shape_functions_face_flux_nodes[idegree][iflux_degree][iface][idim].reinit(n_face_quad_pts, n_dofs);
}
}
}
}
}
template <int dim, int nstate, typename real>
void OperatorBase<dim,nstate,real>::create_metric_basis_operators ()
{
#if 0 //GRID CANNOT BE DEGREE 0
//degree 0 GLL not exist
dealii::QGauss<1> GL (0+1);
// dealii::FE_DGQArbitraryNodes<dim,dim> fe1(GL);
dealii::FE_Q<dim> feq1(GL);
dealii::FESystem<dim,dim> fe1(feq1, dim);
dealii::Quadrature<dim> vol_GL(GL);
const unsigned int n_quad_pts1 = vol_GL.size();
const unsigned int n_dofs1 = fe1.dofs_per_cell;
for(unsigned int iquad=0; iquad<n_quad_pts1; iquad++){
const dealii::Point<dim> grid_node = vol_GL.point(iquad);
const dealii::Point<dim> flux_node = volume_quadrature_collection[0].point(iquad);
for(unsigned int idof=0; idof<n_dofs1; idof++){
mapping_shape_functions_grid_nodes[0][iquad][idof] = fe1.shape_value_component(idof,grid_node,0);
mapping_shape_functions_vol_flux_nodes[0][iquad][idof] = fe1.shape_value_component(idof,flux_node,0);
dealii::Tensor<1,dim,real> derivative;
derivative = fe1.shape_grad_component(idof, grid_node, 0);
for(int idim=0; idim<dim; idim++){
gradient_mapping_shape_functions_grid_nodes[0][idim][iquad][idof] = derivative[idim];
}
}
}
unsigned int n_faces1 = 2.0*dim;
for(unsigned int iface=0; iface<n_faces1; iface++){
const dealii::Quadrature<dim> quadrature1 = dealii::QProjector<dim>::project_to_face(dealii::ReferenceCell::get_hypercube(dim),
face_quadrature_collection[0],
iface);