void Compute_dQdBeta_CTSE(Real* dQdB, SolutionSpace<Real>& space, Int beta)
{
RCmplx perturb(0.0, 1.0e-11);
Mesh<Real>* rm = space.m;
SolutionSpace<RCmplx> cspace(space);
Mesh<RCmplx>* cm = cspace.m;
PObj<RCmplx>* cp = cspace.p;
EqnSet<RCmplx>* ceqnset = cspace.eqnset;
std::vector<SolutionSpaceBase<RCmplx>*> cSolSpaces;
cSolSpaces.push_back(&cspace);
SolutionOrdering<RCmplx> operations;
std::string name = cspace.name;
operations.Insert("Iterate " + name);
operations.Finalize(cSolSpaces);
Int cnnode = cm->GetNumNodes();
Real* dxdb = new Real[cnnode*3];
Get_dXdB(space.param->path+space.param->spacename, dxdb, rm, beta);
//perturb complex part by dxdb*perturb
for(Int i = 0; i < cnnode; i++){
for(Int j = 0; j < 3; j++){
cm->xyz[i*3 + j] += dxdb[i*3 + j]*perturb;
}
}
//update xyz coords
cp->UpdateXYZ(cm->xyz);
//calculate metrics with new grid positions
cm->CalcMetrics();
//create a temporary operations vector with just a single space iterator on it
//run solver
Solve(cSolSpaces, operations);
for(Int i = 0; i < cnnode; i++){
for(Int j = 0; j < ceqnset->neqn; j++){
dQdB[i*ceqnset->neqn + j] =
imag(cspace.q[i*(ceqnset->neqn+ceqnset->nauxvars) + j]) / imag(perturb);
}
}
delete [] dxdb;
return;
}
Real Compute_dObjdX_dXdBeta(SolutionSpace<Real>& space, Int beta)
{
RCmplx perturb (0.0, 1.0e-11);
Real dObjdBeta;
RCmplx Obj;
Mesh<Real>* m = space.m;
EqnSet<Real>* eqnset = space.eqnset;
Param<Real>* param = space.param;
BoundaryConditions<Real>* bc = space.bc;
SolutionSpace<RCmplx> cspace(space);
Mesh<RCmplx>* cm = cspace.m;
PObj<RCmplx>* cp = cspace.p;
EqnSet<RCmplx>* ceqnset = cspace.eqnset;
Int nnode = m->GetNumNodes();
Int cnnode = cm->GetNumNodes();
Real* dxdb = new Real[nnode*3];
Get_dXdB(space.param->path+space.param->spacename, dxdb, m, beta);
//perturb complex part by dxdb*perturb
for(Int i = 0; i < cnnode; i++){
for(Int j = 0; j < 3; j++){
cm->xyz[i*3 + j] += dxdb[i*3 + j]*perturb;
}
}
//update xyz coords
cp->UpdateXYZ(cm->xyz);
//calculate metrics with new grid positions
cm->CalcMetrics();
ComputeSurfaceAreas(&cspace, 0);
Obj = Compute_Obj_Function(cspace);
dObjdBeta = imag(Obj) / imag(perturb);
delete [] dxdb;
return dObjdBeta;
}
void Compute_dQdBeta_FD(Real* dQdB, SolutionSpace<Real>& space, Int beta)
{
Real perturb = 1.0e-8;
Int i ,j;
EqnSet<Real>* eqnset = space.eqnset;
Param<Real>* param = space.param;
Mesh<Real>* m = space.m;
PObj<Real>* p = space.p;
Int nnode = m->GetNumNodes();
std::vector<SolutionSpaceBase<Real>*> solSpaces;
solSpaces.push_back(&space);
//create a temporary operations vector with just a single space iterator on it
SolutionOrdering<Real> operations;
std::string name = space.name;
operations.Insert("Iterate " + name);
operations.Finalize(solSpaces);
//compute dq/db with finite difference
Real* dQdB_up = new Real[nnode*eqnset->neqn];
Real* dQdB_down = new Real[nnode*eqnset->neqn];
Real* Qorig = new Real[nnode*eqnset->neqn];
for(i = 0; i < nnode; i++){
for(j = 0; j < eqnset->neqn; j++){
Qorig[i*eqnset->neqn + j] = space.q[i*(eqnset->neqn+eqnset->nauxvars) + j];
}
}
Real* dxdb = new Real[nnode*3];
Get_dXdB(space.param->path+space.param->spacename, dxdb, m, beta);
//perturb by dxdb*perturb UP
for(Int i = 0; i < nnode; i++){
for(Int j = 0; j < 3; j++){
m->xyz[i*3 + j] += dxdb[i*3 + j]*perturb;
}
}
//update xyz coords
p->UpdateXYZ(m->xyz);
//recalculate metrics
m->CalcMetrics();
//perturb any parameters as required for sensitivities
Perturb_Param(beta, *param, 1);
//reset any interesting field which might depend on perturbations
space.RefreshForParam();
Solve(solSpaces, operations);
for(i = 0; i < nnode; i++){
for(j = 0; j < eqnset->neqn; j++){
dQdB_up[i*eqnset->neqn + j] = space.q[i*(eqnset->neqn+eqnset->nauxvars) + j];
}
}
//perturb by dxdb*perturb DOWN
for(Int i = 0; i < nnode; i++){
for(Int j = 0; j < 3; j++){
m->xyz[i*3 + j] -= 2.0*dxdb[i*3 + j]*perturb;
}
}
//update xyz coords
p->UpdateXYZ(m->xyz);
//recalculate metrics
m->CalcMetrics();
//perturb any parameters as required for sensitivities
//back to original and then down
Perturb_Param(beta, *param, -1);
Perturb_Param(beta, *param, -1);
//reset any interesting field which might depend on perturbations
space.RefreshForParam();
Solve(solSpaces, operations);
for(i = 0; i < nnode; i++){
for(j = 0; j < eqnset->neqn; j++){
dQdB_down[i*eqnset->neqn + j] = space.q[i*(eqnset->neqn+eqnset->nauxvars) + j];
}
}
//compute differences
for(i = 0; i < nnode; i++){
for(j = 0; j < eqnset->neqn; j++){
//up
dQdB_up[i*eqnset->neqn + j] -= Qorig[i*eqnset->neqn + j];
dQdB_up[i*eqnset->neqn + j] /= perturb;
//down
dQdB_down[i*eqnset->neqn + j] -= Qorig[i*eqnset->neqn + j];
dQdB_down[i*eqnset->neqn + j] /= -perturb;
}
}
//average for central difference
for(i = 0; i < nnode; i++){
for(j = 0; j < eqnset->neqn; j++){
dQdB[i*eqnset->neqn + j] =
(dQdB_up[i*eqnset->neqn + j] + dQdB_down[i*eqnset->neqn + j]) / 2.0;
}
}
//reset metrics in case we need them
for(Int i = 0; i < nnode; i++){
for(Int j = 0; j < 3; j++){
m->xyz[i*3 + j] += dxdb[i*3 + j]*perturb;
}
}
//update xyz coords
p->UpdateXYZ(m->xyz);
m->CalcMetrics();
//go back to original value
Perturb_Param(beta, *param, 1);
//reset any interesting field which might depend on perturbations
space.RefreshForParam();
//the gaussian source is sometimes used to modify boundary velocities, etc.
//pre-compute it for bc call
if(space.param->gaussianSource){
space.gaussian->ApplyToResidual();
}
//update boundary conditions
UpdateBCs(&space);
//reset Qorig in case we need it
for(i = 0; i < nnode; i++){
for(j = 0; j < eqnset->neqn; j++){
space.q[i*(eqnset->neqn+eqnset->nauxvars) + j] = Qorig[i*eqnset->neqn + j];
eqnset->ComputeAuxiliaryVariables(&space.q[i*(eqnset->neqn+eqnset->nauxvars)]);
}
}
delete [] Qorig;
delete [] dQdB_up;
delete [] dQdB_down;
delete [] dxdb;
return;
}
void Compute_dRdBeta_CTSE(Real* dRdB, SolutionSpace<Real>& space, Int beta)
{
RCmplx perturb (0.0, 1.0e-11);
Mesh<Real>* rm = space.m;
Int nnode = rm->GetNumNodes();
Int gnode = rm->GetNumParallelNodes();
Int nbnode = rm->GetNumBoundaryNodes();
std::ifstream fin;
SolutionSpace<RCmplx> cspace(space);
Mesh<RCmplx>* cm = cspace.m;
PObj<RCmplx>* cp = cspace.p;
EqnSet<RCmplx>* ceqnset = cspace.eqnset;
Param<RCmplx>* param = cspace.param;
Int cnnode = cm->GetNumNodes();
Int cgnode = cm->GetNumParallelNodes();
Int cnbnode = cm->GetNumBoundaryNodes();
RCmplx* q = cspace.q;
Int neqn = ceqnset->neqn;
Int nvars = neqn + ceqnset->nauxvars;
Real* dxdb = new Real[nnode*3];
Get_dXdB(space.param->path + space.param->spacename, dxdb, rm, beta);
//perturb complex part by dxdb*perturb
for(Int i = 0; i < nnode; i++){
for(Int j = 0; j < 3; j++){
cm->xyz[i*3 + j] += dxdb[i*3 + j]*perturb;
}
}
//update xyz coords
cp->UpdateXYZ(cm->xyz);
//calculate metrics with new grid positions
cm->CalcMetrics();
//compute gradient coefficients once
ComputeNodeLSQCoefficients(&cspace);
//perturb any parameters which we are getting sensitivities for
Perturb_Param(beta, *cspace.param);
//reset any interesting field which might depend on perturbations
cspace.RefreshForParam();
//the gaussian source is sometimes used to modify boundary velocities, etc.
//pre-compute it for bc call
if(cspace.param->gaussianSource){
cspace.gaussian->ApplyToResidual();
}
//update boundary conditions
cspace.p->UpdateGeneralVectors(q, nvars);
UpdateBCs(&cspace);
cspace.p->UpdateGeneralVectors(q, nvars);
//now, compute gradients and limiters
if(param->sorder > 1 || param->viscous){
for(Int i = 0; i < (cnnode+cnbnode+cgnode); i++){
ceqnset->NativeToExtrapolated(&q[i*nvars]);
}
cspace.grad->Compute();
cspace.limiter->Compute(&cspace);
for(Int i = 0; i < (cnnode+cnbnode+cgnode); i++){
ceqnset->ExtrapolatedToNative(&q[i*nvars]);
}
}
//compute spatial residual
SpatialResidual(&cspace);
ExtraSourceResidual(&cspace);
for(Int i = 0; i < nnode; i++){
for(Int j = 0; j < ceqnset->neqn; j++){
dRdB[i*ceqnset->neqn + j] = imag(cspace.crs->b[i*ceqnset->neqn + j])/imag(perturb);
}
}
delete [] dxdb;
}
void ComputedQdBeta_HardsetBC(Int nnodes, Int* nodes, Real* dQdB, const SolutionSpace<Real>& space, Int beta)
{
Real h = 1.0e-11;
RCmplx I(0.0, 1.0);
RCmplx perturb = h*I;
Mesh<Real>* rm = space.m;
SolutionSpace<RCmplx> cspace(space);
Mesh<RCmplx>* cm = cspace.m;
PObj<RCmplx>* cp = cspace.p;
EqnSet<RCmplx>* ceqnset = cspace.eqnset;
Param<RCmplx>* param = cspace.param;
RCmplx* q = cspace.q;
Int nnode = rm->GetNumNodes();
Int neqn = ceqnset->neqn;
Int nvars = neqn + ceqnset->nauxvars;
Real* dxdb = new Real[nnode*3];
Get_dXdB(space.param->path + space.param->spacename, dxdb, rm, beta);
//perturb complex part by dxdb*perturb
for(Int i = 0; i < nnode; i++){
for(Int j = 0; j < 3; j++){
cm->xyz[i*3 + j] += dxdb[i*3 + j]*perturb;
}
}
//update xyz coords
cp->UpdateXYZ(cm->xyz);
//calculate metrics with new grid positions
cm->CalcMetrics();
//compute gradient coefficients once
ComputeNodeLSQCoefficients(&cspace);
//perturb any parameters which we are getting sensitivities for
Perturb_Param(beta, *cspace.param);
//reset any interesting field which might depend on perturbations
cspace.RefreshForParam();
//the gaussian source is sometimes used to modify boundary velocities, etc.
//pre-compute it for bc call
if(cspace.param->gaussianSource){
cspace.gaussian->ApplyToResidual();
}
//update boundary conditions
cspace.p->UpdateGeneralVectors(q, nvars);
UpdateBCs(&cspace);
cspace.p->UpdateGeneralVectors(q, nvars);
for(Int i = 0; i < nnodes; i++){
Int node = nodes[i];
for(Int j = 0; j < neqn; j++){
dQdB[i*neqn + j] = imag(q[node*nvars + j])/h;
std::cout << "dqdb: " << i << ": -" << j << " " << dQdB[i*neqn + j] << std::endl;
}
}
}
Real Compute_dObjdBeta_CTSE(SolutionSpace<Real>& space, SolutionOrdering<Real>& operations, Int beta)
{
Int i;
Real h = 1.0e-11;
RCmplx I(0.0, 1.0);
RCmplx perturb = h*I;
Real dObjdBeta;
RCmplx Obj;
Mesh<Real>* rm = space.m;
Param<Real>* param = space.param;
BoundaryConditions<Real>* bc = space.bc;
PObj<Real>* p = space.p;
Int nnode = rm->GetNumNodes();
SolutionSpace<RCmplx> cspace(space);
Mesh<RCmplx>* cm = cspace.m;
PObj<RCmplx>* cp = cspace.p;
EqnSet<RCmplx>* ceqnset = cspace.eqnset;
Int cnnode = cm->GetNumNodes();
std::cout << "\n\nCOMPUTING dObj/dBeta_CTSE\n" << std::endl;
Real* dxSurf = new Real[nnode*3];
RCmplx* dxSurfC = new RCmplx[nnode*3];
Compute_dXdB_Surface(space.param->path + space.param->spacename, rm, bc, dxSurf, beta);
std::vector<SolutionSpaceBase<RCmplx>*> cSpaces;
cSpaces.push_back(&cspace);
for(i = 0; i < nnode*3; i++){
//perturb complex part by displacement
dxSurfC[i] = dxSurf[i]*perturb;
}
Int smoothingPasses = 1000;
MoveMeshLinearElastic(cm, bc, dxSurfC, smoothingPasses);
cm->CalcMetrics();
//compute gradient coefficients once
ComputeNodeLSQCoefficients(&cspace);
SolutionOrdering<RCmplx> cOperations;
cOperations = operations;
cOperations.Finalize(cSpaces);
//perturb parameters as required
Perturb_Param(beta, *cspace.param);
//reset any interesting field which might depend on perturbations
cspace.RefreshForParam();
//run solver
Solve(cSpaces, cOperations);
Obj = Compute_Obj_Function(cspace);
dObjdBeta = imag(Obj) / h;
std::cout << "\n\nComplex objective function value: " << Obj << std::endl;
delete [] dxSurf;
delete [] dxSurfC;
return dObjdBeta;
}
void Compute_dRdBeta_FD(Real* dRdB, SolutionSpace<Real>& space, Int beta)
{
Real perturb = 1.0e-8;
EqnSet<Real>* eqnset = space.eqnset;
Mesh<Real>* m = space.m;
PObj<Real>* p = space.p;
Param<Real>* param = space.param;
Real* q = space.q;
Int i;
Int neqn = eqnset->neqn;
Int nvars = neqn + eqnset->nauxvars;
Int nnode = m->GetNumNodes();
Int gnode = m->GetNumParallelNodes();
Int nbnode = m->GetNumBoundaryNodes();
Real* Qorig = new Real[nnode*nvars];
Real* resOrig = new Real[nnode*neqn];
Real* resUp = new Real[nnode*neqn];
Real* resDown = new Real[nnode*neqn];
//store original q
for(i = 0; i < (nnode*nvars); i++){
Qorig[i] = space.q[i];
}
UpdateBCs(&space);
//compute spatial residual
SpatialResidual(&space);
ExtraSourceResidual(&space);
for(Int i = 0; i < nnode; i++){
for(Int j = 0; j < eqnset->neqn; j++){
resOrig[i*eqnset->neqn + j] = space.crs->b[i*eqnset->neqn + j];
}
}
Real* dxdb = new Real[nnode*3];
Get_dXdB(space.param->path+space.param->spacename, dxdb, m, beta);
//perturb complex part by dxdb*perturb UP
for(Int i = 0; i < nnode; i++){
for(Int j = 0; j < 3; j++){
m->xyz[i*3 + j] += dxdb[i*3 + j]*perturb;
}
}
//update xyz coords
p->UpdateXYZ(m->xyz);
//calculate metrics with new grid positions
m->CalcMetrics();
//compute gradient coefficients once
ComputeNodeLSQCoefficients(&space);
//perturb parameters as required
Perturb_Param(beta, *(space.param), 1);
//reset any interesting field which might depend on perturbations
space.RefreshForParam();
//the gaussian source is sometimes used to modify boundary velocities, etc.
//pre-compute it for bc call
if(space.param->gaussianSource){
space.gaussian->ApplyToResidual();
}
//update boundary conditions
UpdateBCs(&space);
//now, compute gradients and limiters
if(param->sorder > 1 || param->viscous){
for(Int i = 0; i < (nnode+nbnode+gnode); i++){
eqnset->NativeToExtrapolated(&q[i*nvars]);
}
space.grad->Compute();
space.limiter->Compute(&space);
for(Int i = 0; i < (nnode+nbnode+gnode); i++){
eqnset->ExtrapolatedToNative(&q[i*nvars]);
}
}
//compute spatial residual
SpatialResidual(&space);
ExtraSourceResidual(&space);
for(Int i = 0; i < nnode; i++){
for(Int j = 0; j < eqnset->neqn; j++){
resUp[i*eqnset->neqn + j] = (space.crs->b[i*eqnset->neqn + j]);
}
}
//perturb parameters as required, call twice (move back to original value then perturb down)
Perturb_Param(beta, *(space.param), -1);
Perturb_Param(beta, *(space.param), -1);
//reset any interesting field which might depend on perturbations
space.RefreshForParam();
//the gaussian source is sometimes used to modify boundary velocities, etc.
//pre-compute it for bc call
if(space.param->gaussianSource){
space.gaussian->ApplyToResidual();
}
//perturb complex part by dxdb*perturb DOWN
for(Int i = 0; i < nnode; i++){
for(Int j = 0; j < 3; j++){
m->xyz[i*3 + j] -= 2.0*dxdb[i*3 + j]*perturb;
}
}
//update xyz coords
p->UpdateXYZ(m->xyz);
//calculate metrics with new grid positions
m->CalcMetrics();
//compute gradient coefficients once
ComputeNodeLSQCoefficients(&space);
//update boundary conditions
UpdateBCs(&space);
//now, compute gradients and limiters
if(param->sorder > 1 || param->viscous){
for(Int i = 0; i < (nnode+nbnode+gnode); i++){
eqnset->NativeToExtrapolated(&q[i*nvars]);
}
space.grad->Compute();
space.limiter->Compute(&space);
for(Int i = 0; i < (nnode+nbnode+gnode); i++){
eqnset->ExtrapolatedToNative(&q[i*nvars]);
}
}
//compute spatial residual
SpatialResidual(&space);
ExtraSourceResidual(&space);
for(Int i = 0; i < nnode; i++){
for(Int j = 0; j < eqnset->neqn; j++){
resDown[i*eqnset->neqn + j] = (space.crs->b[i*eqnset->neqn + j]);
}
}
for(Int i = 0; i < nnode; i++){
for(Int j = 0; j < eqnset->neqn; j++){
//up
resUp[i*eqnset->neqn + j] -= resOrig[i*eqnset->neqn + j];
resUp[i*eqnset->neqn + j] /= perturb;
//down
resDown[i*eqnset->neqn + j] -= resOrig[i*eqnset->neqn + j];
resDown[i*eqnset->neqn + j] /= (-perturb);
//central
dRdB[i*eqnset->neqn + j] = (resUp[i*eqnset->neqn + j] + resDown[i*eqnset->neqn +j]) / 2.0;
}
}
//reset metrics in case we need them
for(Int i = 0; i < nnode; i++){
for(Int j = 0; j < 3; j++){
m->xyz[i*3 + j] += dxdb[i*3 + j]*perturb;
}
}
//update xyz coords
p->UpdateXYZ(m->xyz);
//recalculate metrics
m->CalcMetrics();
//compute gradient coefficients once
ComputeNodeLSQCoefficients(&space);
//reset Qorig in case we need it
for(i = 0; i < nnode*nvars; i++){
space.q[i] = Qorig[i];
}
//go back to original values
Perturb_Param(beta, *(space.param), 1);
//reset any interesting field which might depend on perturbations
space.RefreshForParam();
//the gaussian source is sometimes used to modify boundary velocities, etc.
//pre-compute it for bc call
if(space.param->gaussianSource){
space.gaussian->ApplyToResidual();
}
//update boundary conditions
UpdateBCs(&space);
//now, compute gradients and limiters
if(param->sorder > 1 || param->viscous){
for(Int i = 0; i < (nnode+nbnode+gnode); i++){
eqnset->NativeToExtrapolated(&q[i*nvars]);
}
space.grad->Compute();
space.limiter->Compute(&space);
for(Int i = 0; i < (nnode+nbnode+gnode); i++){
eqnset->ExtrapolatedToNative(&q[i*nvars]);
}
}
delete [] dxdb;
delete [] resOrig;
delete [] resUp;
delete [] resDown;
return;
}