Hi
I had a trouble in solving scalar transport equation using DG elements.
For example, I was solving for \lambda in the following equation where *u *is
also a numerical solution
[image: Screen Shot 2019-03-13 at 9.08.17 PM.png]
The thing is I do not get any problem when my mesh file is scale of O(1)
and I have tested my code works fine using the Method of Manufactured
solution.
Yet, when I tried to solve the governing equation at small scale
mesh...(I.e. all (x,y) point in the original mesh-file was reduced by
(0.01x,0.01y)
I receive error like this
An error occurred in line <129> of file
</Users/jaekwangkim/Program/dealii-8.5.0/include/deal.II/lac/sparse_ilu.templates.h>
in function
void dealii::SparseILU<double>::initialize(const
SparseMatrix<somenumber> &, const dealii::SparseILU::AdditionalData &)
[number = double, somenumber = double]
The violated condition was:
luval[ia[k]] != 0
Additional information:
While computing the ILU decomposition, the algorithm found a zero pivot
on the diagonal of row 34. This must stop the ILU algorithm because it
means that the matrix for which you try to compute a decomposition is
singular.
The problem occurs when the red line of the code is executed...
template <int dim>
void StokesProblem<dim>::solve_transport ()
{
std::cout << " -solve transport begins"<< std::endl;
SolverControl solver_control (std::pow(10,6),
system_rhs.block(2).l2_norm() * pow(10,-4));
unsigned int restart = 500;
SolverGMRES< Vector<double> >::AdditionalData
gmres_additional_data(restart+2);
SolverGMRES< Vector<double> > solver(solver_control,
gmres_additional_data);
//make preconditioner
SparseILU<double>::AdditionalData additional_data(0,500); // (0 ,
additional diagonal terms)
std::cout << "B" << std::endl;
SparseILU<double> preconditioner;
*preconditioner.initialize (system_matrix.block(2,2),
additional_data);*
std::cout << "A" << std::endl;
solver.solve (system_matrix.block(2,2), solution.block(2),
system_rhs.block(2), preconditioner);
// constraints.distribute (solution);
}
I wonder now ...
1. why smaller scale mesh only results such error,
2. If possible, is there any choice of better preconditionner for my system
other than SparseILU to go around this problem?
Thanks,
Regards,
Jaekwang Kim
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