# Parallel solver for sparse matrices on unstructured grids

I am trying to solve Euler equations on unstructured grids. Consequently, the problem reduces to solving Ax=b where A is a sparse matrix. Right know I am using Gauss-Seidel (GS) in a serial manner however, I need a parallel code. Since the grid is unstructured I cannot use red-black GS. Is there a fast parallel solver for this kind of situation?

• What about GMRES or BiCGStab methods? Oct 1 '14 at 0:51
• This is a very large question. As nicoguaro mentioned, there are iterative methods like GMRES, BiCGStab, etc. The effectiveness of each of these solvers will depend also on your choice of discretization of the Euler equations, and possibly the physics of your specific problem. Finally, most of the time, you'll need a good preconditioner to get fast convergence. How large is your matrix? There are direct solvers that can work very well on unstructured grids in many cases. Oct 1 '14 at 1:06
• First write your code using PETSc, then later you can easily experiment with solvers/preconditioners. Oct 1 '14 at 15:40
• You may want to look at the answers to this question: scicomp.stackexchange.com/questions/104/…
– Paul
Nov 3 '14 at 17:56