[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

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