[Dune] Problem in implementing parallel linear solver
Kumar, Paras
paras.kumar at fau.de
Tue Dec 5 19:51:34 CET 2017
Hi all,
I'm trying to implement a parallel iterative solver for a LSE based on a
FE discretization for a time depenpendent problem.
It was observed that the number of iterations taken by the iterative
solver to converge varies with the number of processors. This also
affects the accuracy of the computed solution.
For the purpose of simplification, I developed a MWE where I solve the
1D laplacian problem by FE discretization. The code for this example
along with the output for 4 processes is attached for reference.
The matrix A and the rhs vector b are first computed by the master
process and then distributed to all others so that the solution can be
computed in parallel.
Pt-scotch has been used for the data distribution.
Currently, the following preconditioner-solver combination is used :
RestartedGMRES + SSOR
Once, the parallel solver has ended, the solution is computed in serial
at the master processes in order to compare the two.
Here, are a few observations which might give some clues about the error
I make, but I'm not sure.
1. As can be seen in the output file, A is tridiagonal where as the
distributed are not always symmetric.
2. The defect for the solver is different for the parallel and the
serial cases even before the solver starts.
3. The defect differs from the residual(2-norm) [||A-bx||] computed
manually for both the serial and the parallel cases.
Could the members please help understand where I make the error.
With best regards
Paras
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