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eles_hexas.cpp
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/*!
* \file eles_hexas.cpp
* \author - Original code: HiFiLES Aerospace Computing Laboratory (ACL)
* Aero/Astro Department. Stanford University.
* - Current development: Weiqi Shen
* University of Florida
*
* High Fidelity Large Eddy Simulation (HiFiLES) Code.
*
* HiFiLES is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* HiFiLES is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with HiFiLES. If not, see <http://www.gnu.org/licenses/>.
*/
#include <iomanip>
#include <iostream>
#include <cmath>
#include "../include/global.h"
#include "../include/eles_hexas.h"
#include "../include/cubature_1d.h"
#include "../include/cubature_quad.h"
#include "../include/cubature_hexa.h"
using namespace std;
// #### constructors ####
// default constructor
eles_hexas::eles_hexas()
{
}
void eles_hexas::setup_ele_type_specific()
{
#ifndef _MPI
cout << "Initializing hexas" << endl;
#endif
ele_type=4;
n_dims=3;
if (run_input.equation==0)
n_fields=5;
else if (run_input.equation==1)
n_fields=1;
else
FatalError("Equation not supported");
if (run_input.RANS==1)
n_fields++;
n_inters_per_ele=6;
length.setup(12);
n_upts_per_ele=(order+1)*(order+1)*(order+1);
upts_type=run_input.upts_type_hexa;
set_loc_1d_upts();
set_loc_upts();
set_vandermonde1D();
set_vandermonde3D();
//set shock capturing arrays
if (run_input.shock_cap)
{
if (run_input.shock_det == 0)//persson
calc_norm_basis();
else//concentration
FatalError("Shock detector not implemented.");
if (run_input.shock_cap == 1) //exp filter
set_exp_filter();
else
FatalError("Shock capturing method not implemented.");
}
set_inters_cubpts();
set_volume_cubpts(order, loc_volume_cubpts, weight_volume_cubpts);
set_opp_volume_cubpts(loc_volume_cubpts, opp_volume_cubpts);
//de-aliasing by over-integration
if (run_input.over_int)
set_over_int();
n_ppts_per_ele=p_res*p_res*p_res;
n_peles_per_ele=(p_res-1)*(p_res-1)*(p_res-1);
n_verts_per_ele = 8;
set_loc_ppts();
set_opp_p();
n_fpts_per_inter.setup(6);
n_fpts_per_inter(0)=(order+1)*(order+1);
n_fpts_per_inter(1)=(order+1)*(order+1);
n_fpts_per_inter(2)=(order+1)*(order+1);
n_fpts_per_inter(3)=(order+1)*(order+1);
n_fpts_per_inter(4)=(order+1)*(order+1);
n_fpts_per_inter(5)=(order+1)*(order+1);
n_fpts_per_ele=n_inters_per_ele*(order+1)*(order+1);
set_tloc_fpts();
set_tnorm_fpts();
set_opp_0(run_input.sparse_hexa);
set_opp_1(run_input.sparse_hexa);
set_opp_2(run_input.sparse_hexa);
set_opp_3(run_input.sparse_hexa);
if(viscous)
{
// Compute hex filter matrix
if(LES_filter) compute_filter_upts();
set_opp_4(run_input.sparse_hexa);
set_opp_5(run_input.sparse_hexa);
set_opp_6(run_input.sparse_hexa);
temp_grad_u.setup(n_fields,n_dims);
}
temp_u.setup(n_fields);
temp_f.setup(n_fields,n_dims);
}
// #### methods ####
void eles_hexas::set_connectivity_plot()
{
int vertex_0,vertex_1,vertex_2,vertex_3,vertex_4,vertex_5,vertex_6,vertex_7;
int count=0;
int k,l,m;
for(k=0;k<p_res-1;++k){
for(l=0;l<p_res-1;++l){
for(m=0;m<p_res-1;++m){
vertex_0=m+(p_res*l)+(p_res*p_res*k);
vertex_1=vertex_0+1;
vertex_2=vertex_0+p_res+1;
vertex_3=vertex_0+p_res;
vertex_4=vertex_0+p_res*p_res;
vertex_5=vertex_4+1;
vertex_6=vertex_4+p_res+1;
vertex_7=vertex_4+p_res;
connectivity_plot(0,count) = vertex_0;
connectivity_plot(1,count) = vertex_1;
connectivity_plot(2,count) = vertex_2;
connectivity_plot(3,count) = vertex_3;
connectivity_plot(4,count) = vertex_4;
connectivity_plot(5,count) = vertex_5;
connectivity_plot(6,count) = vertex_6;
connectivity_plot(7,count) = vertex_7;
count++;
}
}
}
}
// set location of 1d solution points in standard interval (required for tensor product elements)
void eles_hexas::set_loc_1d_upts(void)
{
cubature_1d cub_1d(upts_type, order);
loc_1d_upts.setup(order + 1);
for (int i = 0; i < order + 1; i++)
loc_1d_upts(i) = cub_1d.get_r(i);
}
// set location of 1d shape points in standard interval (required for tensor product element)
void eles_hexas::set_loc_1d_spts(hf_array<double> &loc_1d_spts, int in_n_1d_spts)
{
int i;
for(i=0;i<in_n_1d_spts;++i)
{
loc_1d_spts(i)=-1.0+((2.0*i)/(1.0*(in_n_1d_spts-1)));
}
}
// set location of solution points in standard element
void eles_hexas::set_loc_upts(void)
{
int i,j,k;
int upt;
loc_upts.setup(n_dims,n_upts_per_ele);
for(i=0;i<(order+1);++i)
{
for(j=0;j<(order+1);++j)
{
for(k=0;k<(order+1);++k)
{
upt=k+(order+1)*j+(order+1)*(order+1)*i;
loc_upts(0,upt)=loc_1d_upts(k);
loc_upts(1,upt)=loc_1d_upts(j);
loc_upts(2,upt)=loc_1d_upts(i);
}
}
}
}
// set location of flux points in standard element
void eles_hexas::set_tloc_fpts(void)
{
int i,j,k;
int fpt;
tloc_fpts.setup(n_dims,n_fpts_per_ele);
for(i=0;i<n_inters_per_ele;++i)
{
for(j=0;j<(order+1);++j)
{
for(k=0;k<(order+1);++k)
{
fpt=k+((order+1)*j)+((order+1)*(order+1)*i);
// for tensor prodiuct elements flux point location depends on solution point location
if(i==0)
{
tloc_fpts(0,fpt)=loc_1d_upts(order-k);
tloc_fpts(1,fpt)=loc_1d_upts(j);
tloc_fpts(2,fpt)=-1.0;
}
else if(i==1)
{
tloc_fpts(0,fpt)=loc_1d_upts(k);
tloc_fpts(1,fpt)=-1.0;
tloc_fpts(2,fpt)=loc_1d_upts(j);
}
else if(i==2)
{
tloc_fpts(0,fpt)=1.0;
tloc_fpts(1,fpt)=loc_1d_upts(k);
tloc_fpts(2,fpt)=loc_1d_upts(j);
}
else if(i==3)
{
tloc_fpts(0,fpt)=loc_1d_upts(order-k);
tloc_fpts(1,fpt)=1.0;
tloc_fpts(2,fpt)=loc_1d_upts(j);
}
else if(i==4)
{
tloc_fpts(0,fpt)=-1.0;
tloc_fpts(1,fpt)=loc_1d_upts(order-k);
tloc_fpts(2,fpt)=loc_1d_upts(j);
}
else if(i==5)
{
tloc_fpts(0,fpt)=loc_1d_upts(k);
tloc_fpts(1,fpt)=loc_1d_upts(j);
tloc_fpts(2,fpt)=1.0;
}
}
}
}
}
void eles_hexas::set_inters_cubpts(void)
{
n_cubpts_per_inter.setup(n_inters_per_ele);
loc_inters_cubpts.setup(n_inters_per_ele);
weight_inters_cubpts.setup(n_inters_per_ele);
tnorm_inters_cubpts.setup(n_inters_per_ele);
cubature_quad cub_quad(0,order);
int n_cubpts_quad = cub_quad.get_n_pts();
for (int i=0;i<n_inters_per_ele;++i)
n_cubpts_per_inter(i) = n_cubpts_quad;
for (int i=0;i<n_inters_per_ele;++i) {
loc_inters_cubpts(i).setup(n_dims,n_cubpts_per_inter(i));
weight_inters_cubpts(i).setup(n_cubpts_per_inter(i));
tnorm_inters_cubpts(i).setup(n_dims,n_cubpts_per_inter(i));
for (int j=0;j<n_cubpts_quad;++j) {
if (i==0) {
loc_inters_cubpts(i)(0,j)=cub_quad.get_r(j);
loc_inters_cubpts(i)(1,j)=cub_quad.get_s(j);
loc_inters_cubpts(i)(2,j)=-1.0;
}
else if (i==1) {
loc_inters_cubpts(i)(0,j)=cub_quad.get_r(j);
loc_inters_cubpts(i)(1,j)=-1.;
loc_inters_cubpts(i)(2,j)=cub_quad.get_s(j);
}
else if (i==2) {
loc_inters_cubpts(i)(0,j)=1.0;
loc_inters_cubpts(i)(1,j)=cub_quad.get_r(j);
loc_inters_cubpts(i)(2,j)=cub_quad.get_s(j);
}
else if (i==3) {
loc_inters_cubpts(i)(0,j)=cub_quad.get_r(j);
loc_inters_cubpts(i)(1,j)=1.0;
loc_inters_cubpts(i)(2,j)=cub_quad.get_s(j);
}
else if (i==4) {
loc_inters_cubpts(i)(0,j)=-1.0;
loc_inters_cubpts(i)(1,j)=cub_quad.get_r(j);
loc_inters_cubpts(i)(2,j)=cub_quad.get_s(j);
}
else if (i==5) {
loc_inters_cubpts(i)(0,j)=cub_quad.get_r(j);
loc_inters_cubpts(i)(1,j)=cub_quad.get_s(j);
loc_inters_cubpts(i)(2,j)=1.0;
}
weight_inters_cubpts(i)(j) = cub_quad.get_weight(j);
if (i==0) {
tnorm_inters_cubpts(i)(0,j)= 0.;
tnorm_inters_cubpts(i)(1,j)= 0.;
tnorm_inters_cubpts(i)(2,j)= -1.;
}
else if (i==1) {
tnorm_inters_cubpts(i)(0,j)= 0.;
tnorm_inters_cubpts(i)(1,j)= -1.;
tnorm_inters_cubpts(i)(2,j)= 0.;
}
else if (i==2) {
tnorm_inters_cubpts(i)(0,j)= 1.;
tnorm_inters_cubpts(i)(1,j)= 0.;
tnorm_inters_cubpts(i)(2,j)= 0.;
}
else if (i==3) {
tnorm_inters_cubpts(i)(0,j)= 0.;
tnorm_inters_cubpts(i)(1,j)= 1.;
tnorm_inters_cubpts(i)(2,j)= 0.;
}
else if (i==4) {
tnorm_inters_cubpts(i)(0,j)= -1.;
tnorm_inters_cubpts(i)(1,j)= 0.;
tnorm_inters_cubpts(i)(2,j)= 0.;
}
else if (i==5) {
tnorm_inters_cubpts(i)(0,j)= 0.;
tnorm_inters_cubpts(i)(1,j)= 0.;
tnorm_inters_cubpts(i)(2,j)= 1.;
}
}
}
set_opp_inters_cubpts();
}
void eles_hexas::set_volume_cubpts(int in_order, hf_array<double> &out_loc_volume_cubpts,hf_array<double> &out_weight_volume_cubpts)
{
cubature_hexa cub_hexa(0,in_order);
int n_cubpts_hexa = cub_hexa.get_n_pts();
out_loc_volume_cubpts.setup(n_dims,n_cubpts_hexa);
out_weight_volume_cubpts.setup(n_cubpts_hexa);
for (int i=0;i<n_cubpts_hexa;++i)
{
out_loc_volume_cubpts(0,i) = cub_hexa.get_r(i);
out_loc_volume_cubpts(1,i) = cub_hexa.get_s(i);
out_loc_volume_cubpts(2,i) = cub_hexa.get_t(i);
out_weight_volume_cubpts(i) = cub_hexa.get_weight(i);
}
}
// Compute the surface jacobian determinant on a face
double eles_hexas::compute_inter_detjac_inters_cubpts(int in_inter,hf_array<double> d_pos)
{
double output = 0.;
double xr, xs, xt;
double yr, ys, yt;
double zr, zs, zt;
double temp0,temp1,temp2;
xr = d_pos(0,0);
xs = d_pos(0,1);
xt = d_pos(0,2);
yr = d_pos(1,0);
ys = d_pos(1,1);
yt = d_pos(1,2);
zr = d_pos(2,0);
zs = d_pos(2,1);
zt = d_pos(2,2);
double xu=0.;
double yu=0.;
double zu=0.;
double xv=0.;
double yv=0.;
double zv=0.;
// From calculus, for a surface parameterized by two parameters
// u and v, than jacobian determinant is
//
// || (xu i + yu j + zu k) cross ( xv i + yv j + zv k) ||
if (in_inter==0) // u=r, v=s
{
xu = xr;
yu = yr;
zu = zr;
xv = xs;
yv = ys;
zv = zs;
}
else if (in_inter==1) // u=r, v=t
{
xu = xr;
yu = yr;
zu = zr;
xv = xt;
yv = yt;
zv = zt;
}
else if (in_inter==2) //u=s, v=t
{
xu = xs;
yu = ys;
zu = zs;
xv = xt;
yv = yt;
zv = zt;
}
else if (in_inter==3) //u=r,v=t
{
xu = xr;
yu = yr;
zu = zr;
xv = xt;
yv = yt;
zv = zt;
}
else if (in_inter==4) //u=s,v=t
{
xu = xs;
yu = ys;
zu = zs;
xv = xt;
yv = yt;
zv = zt;
}
else if (in_inter==5) //u=r,v=s
{
xu = xr;
yu = yr;
zu = zr;
xv = xs;
yv = ys;
zv = zs;
}
temp0 = yu*zv-zu*yv;
temp1 = zu*xv-xu*zv;
temp2 = xu*yv-yu*xv;
output = sqrt(temp0*temp0+temp1*temp1+temp2*temp2);
return output;
}
// set location of plot points in standard element
void eles_hexas::set_loc_ppts(void)
{
int i,j,k;
int ppt;
loc_ppts.setup(n_dims,n_ppts_per_ele);
for(k=0;k<p_res;++k)
{
for(j=0;j<p_res;++j)
{
for(i=0;i<p_res;++i)
{
ppt=i+(p_res*j)+(p_res*p_res*k);
loc_ppts(0,ppt)=-1.0+((2.0*i)/(1.0*(p_res-1)));
loc_ppts(1,ppt)=-1.0+((2.0*j)/(1.0*(p_res-1)));
loc_ppts(2,ppt)=-1.0+((2.0*k)/(1.0*(p_res-1)));
}
}
}
}
// set transformed normal at flux points
void eles_hexas::set_tnorm_fpts(void)
{
int i,j,k;
int fpt;
tnorm_fpts.setup(n_dims,n_fpts_per_ele);
for(i=0;i<n_inters_per_ele;++i)
{
for(j=0;j<(order+1);++j)
{
for(k=0;k<(order+1);++k)
{
fpt=k+((order+1)*j)+((order+1)*(order+1)*i);
if(i==0)
{
tnorm_fpts(0,fpt)=0.0;
tnorm_fpts(1,fpt)=0.0;
tnorm_fpts(2,fpt)=-1.0;
}
else if(i==1)
{
tnorm_fpts(0,fpt)=0.0;
tnorm_fpts(1,fpt)=-1.0;
tnorm_fpts(2,fpt)=0.0;
}
else if(i==2)
{
tnorm_fpts(0,fpt)=1.0;
tnorm_fpts(1,fpt)=0.0;
tnorm_fpts(2,fpt)=0.0;
}
else if(i==3)
{
tnorm_fpts(0,fpt)=0.0;
tnorm_fpts(1,fpt)=1.0;
tnorm_fpts(2,fpt)=0.0;
}
else if(i==4)
{
tnorm_fpts(0,fpt)=-1.0;
tnorm_fpts(1,fpt)=0.0;
tnorm_fpts(2,fpt)=0.0;
}
else if(i==5)
{
tnorm_fpts(0,fpt)=0.0;
tnorm_fpts(1,fpt)=0.0;
tnorm_fpts(2,fpt)=1.0;
}
}
}
}
}
// Filtering operators for use in subgrid-scale modelling
void eles_hexas::compute_filter_upts(void)
{
int i,j,k,l,m,n,N,N2;
double dlt, k_c, sum, norm;
N = order+1;
hf_array<double> X(N), B(N);
hf_array<double> beta(N,N);
filter_upts_1D.setup(N,N);
X = loc_1d_upts;
N2 = N/2;
// If N is odd, round up N/2
if(N % 2 != 0){N2 += 1;}
// Cutoff wavenumber
k_c = 1.0/run_input.filter_ratio;
// Approx resolution in element (assumes uniform point spacing)
// Interval is [-1:1]
dlt = 2.0/order;
// Normalised solution point separation
for (i=0;i<N;++i)
for (j=0;j<N;++j)
beta(j,i) = (X(j)-X(i))/dlt;
// Build high-order-commuting Vasilyev filter
// Only use high-order filters for high enough order
if(run_input.filter_type==0 and N>=3)
{
if (rank==0) cout<<"Building high-order-commuting Vasilyev filter"<<endl;
hf_array<double> C(N);
hf_array<double> A(N,N);
for (i=0;i<N;++i)
{
B(i) = 0.0;
C(i) = 0.0;
for (j=0;j<N;++j)
A(i,j) = 0.0;
}
// Populate coefficient matrix
for (i=0;i<N;++i)
{
// Populate constraints matrix
B(0) = 1.0;
// Gauss filter weights
B(1) = exp(-pow(pi,2)/24.0);
B(2) = -B(1)*pow(pi,2)/k_c/12.0;
if(N % 2 == 1 && i+1 == N2)
B(2) = 0.0;
for (j=0;j<N;++j)
{
A(j,0) = 1.0;
A(j,1) = cos(pi*k_c*beta(j,i));
A(j,2) = -beta(j,i)*pi*sin(pi*k_c*beta(j,i));
if(N % 2 == 1 && i+1 == N2)
A(j,2) = pow(beta(j,i),3);
}
// Enforce filter moments
for (k=3;k<N;++k)
{
for (j=0;j<N;++j)
A(j,k) = pow(beta(j,i),k+1);
B(k) = 0.0;
}
// Solve linear system by inverting A using
// Gauss-Jordan method
gaussj(N,A,B);
for (j=0;j<N;++j)
filter_upts_1D(j,i) = B(j);
}
}
else if(run_input.filter_type==1) // Discrete Gaussian filter
{
if (rank==0) cout<<"Building discrete Gaussian filter"<<endl;
int ctype, index;
double k_R, k_L, coeff;
double res_0, res_L, res_R;
hf_array<double> alpha(N);
cubature_1d cub_1d(0,order);
int n_cubpts_1d = cub_1d.get_n_pts();
hf_array<double> wf(n_cubpts_1d);
for (j=0;j<n_cubpts_1d;j++)
wf(j) = cub_1d.get_weight(j);
// Determine corrected filter width for skewed quadrature points
// using iterative constraining procedure
// ctype options: (-1) no constraining, (0) constrain moment, (1) constrain cutoff frequency
ctype = -1;
if(ctype>=0)
{
for (i=0;i<N2;++i)
{
for (j=0;j<N;++j)
B(j) = beta(j,i);
k_L = 0.1; k_R = 1.0;
res_L = flt_res(N,wf,B,k_L,k_c,ctype);
res_R = flt_res(N,wf,B,k_R,k_c,ctype);
alpha(i) = 0.5*(k_L+k_R);
for (j=0;j<1000;++j)
{
res_0 = flt_res(N,wf,B,k_c,alpha(i),ctype);
if(abs(res_0)<1.e-12) return;
if(res_0*res_L>0.0)
{
k_L = alpha(i);
res_L = res_0;
}
else
{
k_R = alpha(i);
res_R = res_0;
}
if(j==999)
{
alpha(i) = k_c;
ctype = -1;
}
}
alpha(N-i-1) = alpha(i);
}
}
else if(ctype==-1) // no iterative constraining
for (i=0;i<N;++i)
alpha(i) = k_c;
sum = 0.0;
for (i=0;i<N;++i)
{
norm = 0.0;
for (j=0;j<N;++j)
{
filter_upts_1D(i,j) = wf(j)*exp(-6.0*pow(alpha(i)*beta(i,j),2));
norm += filter_upts_1D(i,j);
}
for (j=0;j<N;++j)
{
filter_upts_1D(i,j) /= norm;
sum += filter_upts_1D(i,j);
}
}
}
else if(run_input.filter_type==2) // Modal coefficient filter
{
if (rank==0) cout<<"Building modal filter"<<endl;
// Compute restriction-prolongation filter
compute_modal_filter_1d(filter_upts_1D, vandermonde1D, inv_vandermonde1D, N, order);
sum = 0;
for(i=0;i<N;i++)
for(j=0;j<N;j++)
sum+=filter_upts_1D(i,j);
}
else // Simple average for low order
{
if (rank==0) cout<<"Building average filter"<<endl;
sum=0;
for (i=0;i<N;i++)
{
for (j=0;j<N;j++)
{
filter_upts_1D(i,j) = 1.0/N;
sum+=1.0/N;
}
}
}
// Build 3D filter on ideal (reference) element.
// This construction is unique to hexa elements but the resulting
// matrix will be of the same(?) dimension for all 3D element types.
int ii=0;
filter_upts.setup(n_upts_per_ele,n_upts_per_ele);
sum=0;
for (i=0;i<N;++i)
{
for (j=0;j<N;++j)
{
for (k=0;k<N;++k)
{
int jj=0;
for (l=0;l<N;++l)
{
for (m=0;m<N;++m)
{
for (n=0;n<N;++n)
{
filter_upts(ii,jj) = filter_upts_1D(k,n)*filter_upts_1D(j,m)*filter_upts_1D(i,l);
sum+=filter_upts(ii,jj);
++jj;
}
}
}
++ii;
}
}
}
}
//#### helper methods ####
int eles_hexas::read_restart_info_ascii(ifstream& restart_file)
{
string str;
// Move to triangle element
while(1) {
getline(restart_file,str);
if (str=="HEXAS") break;
if (restart_file.eof()) return 0;
}
getline(restart_file,str);
restart_file >> order_rest;
getline(restart_file,str);
getline(restart_file,str);
restart_file >> n_upts_per_ele_rest;
getline(restart_file,str);
getline(restart_file,str);
loc_1d_upts_rest.setup(order_rest+1);
for (int i=0;i<order_rest+1;++i)
restart_file >> loc_1d_upts_rest(i);
set_opp_r();
return 1;
}
#ifdef _HDF5
void eles_hexas::read_restart_info_hdf5(hid_t &restart_file, int in_rest_order)
{
hid_t dataset_id, plist_id;
//open dataset
dataset_id = H5Dopen2(restart_file, "HEXAS", H5P_DEFAULT);
if (dataset_id < 0)
FatalError("Cannot find hexa element property");
plist_id = H5Pcreate(H5P_DATASET_XFER);
#ifdef _MPI
//set collective read
H5Pset_dxpl_mpio(plist_id, H5FD_MPIO_COLLECTIVE);
#endif
if (n_eles)
{
order_rest = in_rest_order;
n_upts_per_ele_rest = (order_rest + 1) * (order_rest + 1) * (order_rest + 1);
loc_1d_upts_rest.setup(order_rest + 1);
//read data
H5Dread(dataset_id, H5T_NATIVE_DOUBLE, H5S_ALL, H5S_ALL, plist_id, loc_1d_upts_rest.get_ptr_cpu());
set_opp_r();
}
#ifdef _MPI
else //read empty
{
hid_t null_id=H5Dget_space(dataset_id);
H5Sselect_none(null_id);
H5Dread(dataset_id, H5T_NATIVE_DOUBLE, null_id, null_id, plist_id, NULL);
H5Sclose(null_id);
}
#endif
//close objects
H5Pclose(plist_id);
H5Dclose(dataset_id);
}
#endif
// write restart info
#ifndef _HDF5
void eles_hexas::write_restart_info_ascii(ofstream& restart_file)
{
restart_file << "HEXAS" << endl;
restart_file << "Order" << endl;
restart_file << order << endl;
restart_file << "Number of solution points per hexahedral element" << endl;
restart_file << n_upts_per_ele << endl;
restart_file << "Location of solution points in 1D" << endl;
for (int i=0;i<order+1;++i) {
restart_file << loc_1d_upts(i) << " ";
}
restart_file << endl;
}
#endif
#ifdef _HDF5
void eles_hexas::write_restart_info_hdf5(hid_t &restart_file)
{
hid_t dataset_id,plist_id,dataspace_id;
hsize_t dim = run_input.order + 1;
//create HEXAS dataset
dataspace_id = H5Screate_simple(1, &dim, NULL);
dataset_id = H5Dcreate2(restart_file, "HEXAS", H5T_NATIVE_DOUBLE, dataspace_id, H5P_DEFAULT, H5P_DEFAULT, H5P_DEFAULT);
plist_id = H5Pcreate(H5P_DATASET_XFER);
#ifdef _MPI
//set collective read
H5Pset_dxpl_mpio(plist_id, H5FD_MPIO_COLLECTIVE);
#endif
//write loc_1d_upts
if(n_eles)
{
H5Dwrite(dataset_id,H5T_NATIVE_DOUBLE,H5S_ALL,H5S_ALL,plist_id,loc_1d_upts.get_ptr_cpu());
}
#ifdef _MPI
else
{
H5Sselect_none(dataspace_id);
H5Dwrite(dataset_id,H5T_NATIVE_DOUBLE,dataspace_id,dataspace_id,plist_id,NULL);
}
#endif
H5Pclose(plist_id);
H5Dclose(dataset_id);
H5Sclose(dataspace_id);
}
#endif
// initialize the vandermonde matrix
void eles_hexas::set_vandermonde1D(void)
{
vandermonde1D.setup(order+1,order+1);
for (int i=0;i<order+1;i++)
for (int j=0;j<order+1;j++)
vandermonde1D(i,j) = eval_legendre(loc_1d_upts(i),j);
// Store its inverse
inv_vandermonde1D = inv_array(vandermonde1D);
}
void eles_hexas::set_vandermonde3D(void)
{
vandermonde.setup(n_upts_per_ele,n_upts_per_ele);
hf_array<double> loc(n_dims);
for (int i=0;i<n_upts_per_ele;i++)//location
{
loc(0)=loc_upts(0,i);
loc(1)=loc_upts(1,i);
loc(2)=loc_upts(2,i);
for (int j=0;j<n_upts_per_ele;j++)//in mode
vandermonde(i,j)=eval_legendre_basis_3D_hierarchical(j,loc,order);
}
inv_vandermonde=inv_array(vandermonde);
}
void eles_hexas::set_exp_filter(void)
{
exp_filter.setup(n_upts_per_ele, n_upts_per_ele);
exp_filter.initialize_to_zero();
int i, j, k, l, mode;
double eta_x, eta_y, eta_z;
double eta_c = (double)run_input.expf_cutoff / (double)(order);
mode = 0;
for (l = 0; l < 3 * order + 1; l++) //sum of x,y,z mode
{
for (k = 0; k < l + 1; k++) //k no more than sum
{
for (j = 0; j < l - k + 1; j++) //j no more than sum-k
{
i = l - k - j; //i+j+k=l
if (i <= order && j <= order && k <= order)
{
eta_x = (double)(i) / (double)(order);
eta_y = (double)(j) / (double)(order);
eta_z = (double)(k) / (double)(order);
exp_filter(mode, mode) = 1.;
if (eta_x > eta_c)
exp_filter(mode, mode) *= exp(-run_input.expf_fac * pow((eta_x - eta_c) / (1. - eta_c), run_input.expf_order));
if (eta_y > eta_c)
exp_filter(mode, mode) *= exp(-run_input.expf_fac * pow((eta_y - eta_c) / (1. - eta_c), run_input.expf_order));
if (eta_z > eta_c)
exp_filter(mode, mode) *= exp(-run_input.expf_fac * pow((eta_z - eta_c) / (1. - eta_c), run_input.expf_order));
mode++;
}
}
}
}
exp_filter = mult_arrays(exp_filter, inv_vandermonde);
exp_filter = mult_arrays(vandermonde, exp_filter);
}
void eles_hexas::calc_norm_basis(void)
{
int n1, n2, n3;
double norm1, norm2, norm3;
norm_basis_persson.setup(n_upts_per_ele);
for (int i = 0; i < n_upts_per_ele; i++)
{
get_legendre_basis_3D_index(i, order, n1, n2, n3);
norm1 = 2.0 / (2.0 * n1 + 1.0);
norm2 = 2.0 / (2.0 * n2 + 1.0);