SolutionInstance TubeLF::Integrate(d dt) {
// Integrate using Lax-Friedrich method
d t=sol.getTime();
d newt = t + dt;
// Define new solutioninstance
SolutionInstance newsol(gp);
newsol.setTime(newt);
const vd& oldrho=sol.rho();
const vd& oldm=sol.m();
const vd& oldrhoE=sol.rhoE();
vd& rho=newsol.rho_ref();
vd& m=newsol.m_ref();
vd& rhoE=newsol.rhoE_ref();
// Fluxes from previous solution
vd Cflux=sol.Cflux();
vd Mflux=sol.Mflux();
vd Eflux=sol.Eflux();
{ // Left boundary
d la = dt/dx;
rho(0) = oldrho(0);
rho(0)+=-la*(Cflux(1)-Cflux(0));
d oldu0=oldm(0)/oldrho(0);
// std::cout << "oldu:"<< oldu0 << std::endl;
d momfluxl = pow(oldm(0), 2)/oldrho(0) + pleft(t);
m(0) = oldm(0);
m(0)+=-la*(Mflux(1)-momfluxl);
rhoE(0) = oldrhoE(0);
rhoE(0)+=-la*(Eflux(1)-Eflux(0));
} // End left boundary
{ // Inner nodes
d lambda = dt/(2*dx);
rho.subvec(1,gp-2)=0.5*(oldrho.head(gp-2) + oldrho.tail(gp-2));
rho.subvec(1,gp-2)+=-lambda*(Cflux.tail(gp-2) -Cflux.head(gp-2));
m.subvec(1,gp-2)=0.5*(oldm.head(gp-2) + oldm.tail(gp-2));
m.subvec(1,gp-2)+=-lambda*(Mflux.tail(gp-2) -Mflux.head(gp-2));
rhoE.subvec(1,gp-2)=0.5*(oldrhoE.head(gp-2) + oldrhoE.tail(gp-2));
rhoE.subvec(1,gp-2)+=-lambda*(Eflux.tail(gp-2) -Eflux.head(gp-2));
} // End inner nodes
{ // Right boundary
int i = gp - 1;
d la = dt/dx;
rho(i) = oldrho(i);
rho(i)+=-la*(0-Cflux(i-1));
m(i) = 0;
rhoE(i) = oldrhoE(i);
rhoE(i)+=-la*(0-Eflux(i-1));
} // End right boundary
return newsol;
}
SolutionInstance TubeMCM::Integrate(d dt){ // Integrate using
// MacCormack method
d t=sol.getTime();
d newt=t+dt;
d lambda=dt/dx;
SolutionInstance predictor(gp);
{ // Predictor step
const vd& oldrho=sol.rho();
const vd& oldm=sol.m();
const vd& oldrhoE=sol.rhoE();
vd& prho=predictor.rho_ref();
vd& pm=predictor.m_ref();
vd& prhoE=predictor.rhoE_ref();
// Fluxes from previous solution
vd Cflux=sol.Cflux();
vd Mflux=sol.Mflux();
vd Eflux=sol.Eflux();
// Density
prho.tail(gp-1)=oldrho.tail(gp-1)
-lambda*(Cflux.tail(gp-1)-Cflux.head(gp-1));
// The first element
prho(0)=oldrho(0)-lambda*(Cflux(1)-Cflux(0));
// Momentum
d oldu0=oldm(0)/oldrho(0);
d momfluxl = pow(oldm(0), 2)/oldrho(0) + pleft(t);
pm.tail(gp-1)=oldm.tail(gp-1)
-lambda*(Mflux.tail(gp-1)-Mflux.head(gp-1));
// The first element
pm(0)=oldm(0)-lambda*(Mflux(1)-momfluxl);
pm(gp-1)=0;
// Energy
prhoE.tail(gp-1)=oldrhoE.tail(gp-1)
-lambda*(Eflux.tail(gp-1)-Eflux.head(gp-1));
// The first element
prhoE(0)=oldrhoE(0)-lambda*(Eflux(1)-Eflux(0));
}
SolutionInstance corrector(gp);
// Temp test hack:
corrector=predictor;
corrector.setTime(newt);
return corrector;
} // Integrate(dt)
ordinal_type
Stokhos::CGDivisionExpansionStrategy<ordinal_type,value_type,node_type>::
CG(const Teuchos::SerialDenseMatrix<ordinal_type, value_type> & A,
Teuchos::SerialDenseMatrix<ordinal_type,value_type> & X,
const Teuchos::SerialDenseMatrix<ordinal_type,value_type> & B,
ordinal_type max_iter,
value_type tolerance,
ordinal_type prec_iter,
ordinal_type order ,
ordinal_type m,
ordinal_type PrecNum,
const Teuchos::SerialDenseMatrix<ordinal_type, value_type> & M,
ordinal_type diag)
{
ordinal_type n = A.numRows();
ordinal_type k=0;
value_type resid;
Teuchos::SerialDenseMatrix<ordinal_type, value_type> Ax(n,1);
Ax.multiply(Teuchos::NO_TRANS,Teuchos::NO_TRANS,1.0, A, X, 0.0);
Teuchos::SerialDenseMatrix<ordinal_type, value_type> r(Teuchos::Copy,B);
r-=Ax;
resid=r.normFrobenius();
Teuchos::SerialDenseMatrix<ordinal_type, value_type> p(r);
Teuchos::SerialDenseMatrix<ordinal_type, value_type> rho(1,1);
Teuchos::SerialDenseMatrix<ordinal_type, value_type> oldrho(1,1);
Teuchos::SerialDenseMatrix<ordinal_type, value_type> pAp(1,1);
Teuchos::SerialDenseMatrix<ordinal_type, value_type> Ap(n,1);
value_type b;
value_type a;
while (resid > tolerance && k < max_iter){
Teuchos::SerialDenseMatrix<ordinal_type, value_type> z(r);
//Solve Mz=r
if (PrecNum != 0){
if (PrecNum == 1){
Stokhos::DiagPreconditioner<ordinal_type, value_type> precond(M);
precond.ApplyInverse(r,z,prec_iter);
}
else if (PrecNum == 2){
Stokhos::JacobiPreconditioner<ordinal_type, value_type> precond(M);
precond.ApplyInverse(r,z,2);
}
else if (PrecNum == 3){
Stokhos::GSPreconditioner<ordinal_type, value_type> precond(M,0);
precond.ApplyInverse(r,z,1);
}
else if (PrecNum == 4){
Stokhos::SchurPreconditioner<ordinal_type, value_type> precond(M, order, m, diag);
precond.ApplyInverse(r,z,prec_iter);
}
}
rho.multiply(Teuchos::TRANS,Teuchos::NO_TRANS,1.0, r, z, 0.0);
if (k==0){
p.assign(z);
rho.multiply(Teuchos::TRANS, Teuchos::NO_TRANS, 1.0, r, z, 0.0);
}
else {
b=rho(0,0)/oldrho(0,0);
p.scale(b);
p+=z;
}
Ap.multiply(Teuchos::NO_TRANS,Teuchos::NO_TRANS,1.0, A, p, 0.0);
pAp.multiply(Teuchos::TRANS,Teuchos::NO_TRANS,1.0, p, Ap, 0.0);
a=rho(0,0)/pAp(0,0);
Teuchos::SerialDenseMatrix<ordinal_type, value_type> scalep(p);
scalep.scale(a);
X+=scalep;
Ap.scale(a);
r-=Ap;
oldrho.assign(rho);
resid=r.normFrobenius();
k++;
}
//std::cout << "iteration count " << k << std::endl;
return 0;
}
// CG
int CG(const Teuchos::SerialDenseMatrix<int, double> & A, Teuchos::SerialDenseMatrix<int,double> X,const Teuchos::SerialDenseMatrix<int,double> & B, int max_iter, double tolerance, Stokhos::DiagPreconditioner<int,double> prec)
{
int n;
int k=0;
double resid;
n=A.numRows();
std::cout << "A= " << A << std::endl;
std::cout << "B= " << B << std::endl;
Teuchos::SerialDenseMatrix<int, double> Ax(n,1);
Ax.multiply(Teuchos::NO_TRANS,Teuchos::NO_TRANS,1.0, A, X, 0.0);
Teuchos::SerialDenseMatrix<int, double> r(B);
r-=Ax;
resid=r.normFrobenius();
Teuchos::SerialDenseMatrix<int, double> rho(1,1);
Teuchos::SerialDenseMatrix<int, double> oldrho(1,1);
Teuchos::SerialDenseMatrix<int, double> pAp(1,1);
Teuchos::SerialDenseMatrix<int, double> Ap(n,1);
double b;
double a;
Teuchos::SerialDenseMatrix<int, double> p(r);
while (resid > tolerance && k < max_iter){
Teuchos::SerialDenseMatrix<int, double> z(r);
//z=M-1r
// prec.ApplyInverse(r,z);
rho.multiply(Teuchos::TRANS,Teuchos::NO_TRANS,1.0, r, z, 0.0);
if (k==0){
p.assign(z);
rho.multiply(Teuchos::TRANS, Teuchos::NO_TRANS, 1.0, r, z, 0.0);
}
else {
b=rho(0,0)/oldrho(0,0);
p.scale(b);
p+=z;
}
Ap.multiply(Teuchos::NO_TRANS,Teuchos::NO_TRANS,1.0, A, p, 0.0);
pAp.multiply(Teuchos::TRANS,Teuchos::NO_TRANS,1.0, p, Ap, 0.0);
a=rho(0,0)/pAp(0,0);
Teuchos::SerialDenseMatrix<int, double> scalep(p);
scalep.scale(a);
X+=scalep;
Ap.scale(a);
r-=Ap;
oldrho.assign(rho);
resid=r.normFrobenius();
k++;
}
std::cout << "X= " << X << std::endl;
return 0;
}
