# Parallel solution of PDEs

Which is the best approach to solve a PDE in parallel:

1.To split the mesh the mesh in N parts and every processor works on its own part or

2.To take the global linear system Ax=b and solve it in parallel

• Either approach can be better — or they can be equivalent. It depends on how you discretize and how you parallelize. Apr 22 '20 at 9:07

The second approach of course also has to split the mesh somehow because the linear system $$Ax=b$$ does not magically appear out of thin air, but needs to be constructed and that is also done by partitioning the mesh.
• I want to expend on Wolfgang's answer. You should definitely use approach 2. However, you should have a holistic approach. Do not try to assemble the matrix $A$ on a single process and distribute. If you check popular packages like hypre, PETSc, MFEM, ngsolve, fenics, ..., all of them distribute the mesh, assemble the local matrices and then assemble global matrix. See the figure at mfem.org/performance . Then you can natively solve the problem $Ax=b$ in parallel. Apr 23 '20 at 2:28