An alternative approach of parallel preconditioning for 2D finite element problems

We propose an alternative approach of parallel preconditioning for 2D finite element problems. This technique consists in a proper domain decomposition with reordering that produces narrowband linear systems from finite element discretization, allowing to apply, without significant efforts, traditional preconditioners as Incomplete LU Factorization (ILU) or even sophisticated parallel preconditioners as SPIKE. Another feature of that approach is the facility to recalculate finite element matrices whether for nonlinear corrections or for time integration schemes. That means parallel finite element application is performed indeed in parallel, not just to solve the linear system. We also employ preconditioners based on element-by-element storage with minimal adjustments. Robustness and scalability of these parallel preconditioning strategies are demonstrated for a set of benchmark experiments. We consider a group of two-dimensional fluid flow problems modeled by transport, and Euler equations to evaluate ILU, SPIKE, and some element-by-element preconditioners. Moreover, our approach provides load balancing and improvement to MPI communications. We study the load balancing and MPI communications through analyzer tools as TAU (Tuning Analysis Utilities)