void Plot(ADERDG* adg)
{
FILE * gnufile;
gnufile = fopen("adgplot.dat", "w" );
for(int ie = 1; ie <= _NBELEMS_IN; ie++){
for(int j = 0; j < _NGLOPS; j++){
double wex[_M];
double h = adg->face[ie] - adg->face[ie-1];
double x = adg->face[ie-1] + h * gauss_lob_point[gauss_lob_offset[_D]+j];
ExactSol(x, adg->tnow, wex);
fprintf(gnufile, "%f ", x);
//printf("ie=%d j=%d x=%f\n",ie,j, x);
// numerical values
for (int iv = 0; iv < _M; ++iv){
fprintf(gnufile, "%f ", adg->wnow[ie][j][iv]);
}
// exact values
for (int iv=0;iv<_M;++iv){
fprintf(gnufile,"%f ",wex[iv]);
}
// predictor (debug)
for (int iv = 0; iv < _M; ++iv){
fprintf(gnufile, "%f ", adg->wpred[ie][j][iv]);
}
fprintf(gnufile,"\n");
}
}
fclose(gnufile);
}
void InitADERDG(ADERDG* adg, double xmin, double xmax)
{
adg->xmin = xmin;
adg->xmax = xmax;
for(int i = 0; i < _NBFACES; i++) {
double xh = (double)i / _NBELEMS_IN;
double x = stretching(xh);
adg->face[i] = xmin + x * (xmax - xmin);
//printf("i=%d x=%f\n",i, adg->face[i]);
}
adg->dx = 0.0;
for(int ie = 1; ie <= _NBELEMS_IN; ie++) {
adg->dx = _MAX(adg->dx, adg->face[ie] - adg->face[ie - 1]);
}
adg->cfl = _CFL;
adg->dt = adg->cfl * adg->dx; // TODO: put the velocity
adg->ncfl = 0;
for(int ie = 1; ie <= _NBELEMS_IN; ie++) {
adg->cell_level[ie] =
(int) (log(adg->dx / (adg->face[ie] - adg->face[ie-1])) / log(2));
adg->ncfl = _MAX ( adg->ncfl , adg->cell_level[ie] );
}
// convention: first and last cell are among the biggest elements
adg->cell_level[0] = 0;
adg->cell_level[_NBELEMS_IN + 1] = 0;
printf("found %d cfl levels\n", adg->ncfl);
adg->dt_small = adg->dt / (1 << adg->ncfl);
printf("small dt=%f max cell size=%f\n", adg->dt_small, adg->dx);
for(int ie = 1; ie <= _NBELEMS_IN; ie++) {
for(int j = 0;j < _NGLOPS; j++) {
double h = adg->face[ie] - adg->face[ie-1];
double x = adg->face[ie-1]
+ h * gauss_lob_point[gauss_lob_offset[_D] + j];
ExactSol(x, 0, adg->wnow[ie][j]);
}
}
for(int ie = 1;ie <= _NBELEMS; ie++){
for(int j = 0;j < _NGLOPS; j++){
for(int iv = 0; iv < _M; iv++){
adg->wnext[ie][j][iv] = adg->wnow[ie][j][iv];
}
}
}
for(int i=0;i<_NBFACES;i++){
adg->face_level[i]=_MAX(adg->cell_level[i],adg->cell_level[i+1]);
}
}
/**
* @brief
* Calculate the Norm Error of Numerical Solution at Spicific Time.
*/
void NormErr(structMesh *mesh, physics *phys,
double time, double **c,
double *L2, double *Linf) {
double **temp = Matrix_create(mesh->ndim1, mesh->ndim2);
ExactSol(mesh, phys, time, temp);
double err = 0;
double maxerr = 0.0;
int dim1, dim2;
for (dim1=0; dim1<mesh->ndim1; dim1++) {
for (dim2=0; dim2<mesh->ndim2; dim2++) {
double dc = c[dim1][dim2]-temp[dim1][dim2];
maxerr = maxf(fabs(dc), maxerr);
err += dc*dc;
}
}
*L2 = sqrt(err/mesh->ndim1/mesh->ndim2);
*Linf = maxerr;
Matrix_free(temp);
return;
}
void ADERTimeStep(ADERDG* adg)
{
double dt = adg->dt_small;
// first, predict the values of w at an intermediate time step
for(int ie = 1;ie <= _NBELEMS_IN; ie++) {
Predictor(adg, ie, dt / 2);
}
// init the derivative to zero
for(int ie = 1; ie<= _NBELEMS_IN; ie++) {
for(int i = 0; i < _NGLOPS; i++) {
for(int iv = 0; iv < _M; iv++) {
adg->dtw[ie][i][iv]=0;
}
}
}
// impose the exact values on boundary left and right cells
double x = adg->face[0];
double t = adg->tnow + dt / 2 ;
ExactSol(x, t, adg->wpred[0][_D]); // _D = last point of left cell
x = adg->face[_NBFACES-1];
// 0 = first point of right cell
ExactSol(x, t, adg->wpred[_NBELEMS_IN + 1][0]);
// compute the face flux terms
// loop on the faces
for(int i = 0; i < _NBFACES; i++){
double *wL, *wR;
double flux[_M];
int ie = i;
wL = adg->wpred[ie][_D]; // _D = last point of left cell
wR = adg->wpred[ie+1][0]; // 0 = first point of right cell
NumFlux(wL, wR, flux);
for (int k = 0; k < _M; k++){
adg->dtw[ie][_D][k] -= flux[k];
adg->dtw[ie+1][0][k] += flux[k];
}
}
// compute the volume terms
for(int ie = 1; ie<= _NBELEMS_IN; ie++){
double h = adg->face[ie] - adg->face[ie-1];
// loop on the glops i
for(int i = 0; i < _NGLOPS; i++){
// integration weight
double omega = wglop(_D, i) * h;
// flux at glop i
double flux[_M];
NumFlux(adg->wpred[ie][i], adg->wpred[ie][i], flux);
// loop on the basis functions j
for(int j = 0; j < _D+1; j++){
// derivative of basis function j at glop i
double dd = dlag(_D, j, i) / h;
for (int k = 0; k < _M; k++){
adg->dtw[ie][j][k] += omega * dd * flux[k];
}
}
}
}
// divide by the mass matrix
for(int ie = 1; ie<= _NBELEMS_IN; ie++){
double h = adg->face[ie] - adg->face[ie-1];
for(int i = 0; i < _NGLOPS; i++){
double omega = wglop(_D, i) * h;
for (int k = 0; k < _M; k++){
adg->dtw[ie][i][k] /= omega;
}
}
}
// update wnext and
// copy wnext into wnow for the next time step
for(int ie = 1; ie<= _NBELEMS_IN; ie++){
for(int i = 0; i < _NGLOPS; i++){
for(int iv = 0; iv < _M; iv++){
adg->wnext[ie][i][iv] =
adg->wnow[ie][i][iv] + dt * adg->dtw[ie][i][iv];
adg->wnow[ie][i][iv] = adg->wnext[ie][i][iv];
}
}
}
}