NumProcFluxError ( shared_ptr<PDE> apde, const Flags & flags) : NumProc(apde) {
fes = GetPDE()->GetFESpace(flags.GetStringFlag("fespace",NULL));
ext = GetPDE()->GetFESpace(flags.GetStringFlag("extensionspace",NULL));
hdivip = GetPDE()->GetBilinearForm(flags.GetStringFlag("hdivproduct",NULL));
q = GetPDE()->GetGridFunction(flags.GetStringFlag("discreteq",NULL));
Q = GetPDE()->GetGridFunction(flags.GetStringFlag("exactq",NULL));
err = GetPDE()->GetGridFunction(flags.GetStringFlag("errorsquareq",NULL));
}
void Do(LocalHeap & lh) {
// We proceed in three steps:
// 1. Compute the difference between Q and q
// 2. Compute the H(div) Schur complement
// 3. Apply Schur complement to the difference
// grid function with (interpolated) exact flux, grad(u)
BaseVector& vecQ = Q->GetVector();
// numerical flux q
BaseVector& vecq = q->GetVector();
// p.w. constant gridfunction to store element-wise error
BaseVector& errvec = err->GetVector();
errvec.FV<double>() = 0.0;
double sqer =0.0; // this will contain the total error square
for(int k=0; k<ma->GetNE(); k++) {
ElementId ei (VOL, k);
double elndof = ext->GetFE(k,lh).GetNDof();
Vector<SCAL> diff(elndof);
// dof nrs: global, global inner, local inner, local Schur
Array<int> Gn, Ginn, Linn, Lsn;
// compute the difference between Q and q
ext->GetDofNrs(k,Gn); // Global# of all dofs on element k
diff = SCAL(0.0);
for(int j=0; j<elndof; j++)
diff[j] = vecQ.FV<SCAL>()[Gn[j]] - vecq.FV<SCAL>()[Gn[j]];
// H(div) Gram matrix (given in two parts in pde file)
Matrix<double> elmat(elndof), elmat2(elndof);
elmat = 0.0; elmat2 = 0.0;
hdivip->GetIntegrator(0)->
CalcElementMatrix(ext->GetFE(ei,lh),ma->GetTrafo(ei,lh),elmat,lh);
hdivip->GetIntegrator(1)->
CalcElementMatrix(ext->GetFE(ei,lh),ma->GetTrafo(ei,lh),elmat2,lh);
elmat += elmat2;
// compute the H(div) Schur complement
ext->GetInnerDofNrs(k,Ginn); // Global# of inner dofs on element k
for(int j=0; j<elndof; j++)
if (Ginn.Contains( Gn[j] ))
Linn.Append(j); // Local# of inner dofs on element k
else
Lsn.Append(j); // Local# of Schur dofs on element k
int ielndof = Linn.Size();
Matrix<double> elmati(ielndof),elmatiinv(ielndof);
elmati = elmat.Rows(Linn).Cols(Linn);
CalcInverse(elmati,elmatiinv);
// apply Schur complement to the difference
int selndof = elndof - ielndof;
Vector<SCAL> diffs(selndof);
Matrix<double> S(selndof), Asi(selndof,ielndof);
diffs = diff(Lsn);
// S = A_ss - A_si * inv(A_ii) * A_is
Asi = elmat.Rows(Lsn).Cols(Linn);
S = elmat.Rows(Lsn).Cols(Lsn);
S -= Asi * elmatiinv * Trans(Asi);
// error = (S * diffs, diffs)
errvec.FVDouble()[k] = fabs(InnerProduct(diffs, S * diffs));
sqer += errvec.FVDouble()[k];
}
cout<<"Discrete H^(-1/2) norm of error in q = "<<sqrt(sqer)<<endl;
// write file (don't know what the last argument of AddVariable
// does, but 6 seems to be the value everywhere! It seems to intializes
// an object of class IM (important message).
GetPDE()->AddVariable (string("fluxerr.")+GetName()+".value", sqrt(sqer), 6);
}
/*
* Set value to a page directory entry
* Note: No TLB purge/cache operations are performed here.
*/
Inline void SetPDE( const void* laddr, PDE pde_v )
{
PDE* pde = GetPDE(laddr);
*pde = pde_v;
}
