Comparative Analysis of High Performance Solvers for 3D Elliptic Problems

Abstract. The presented comparative analysis concerns two iterative solvers for 3D linear boundary value problems of elliptic type. After applying the Finite Difference Method (FDM) or the Finite Element Method (FEM) discretization a system of linear algebraic equations has to be solved, where the stiffness matrix is large, sparse and symmetric positive definite. It is well known that the preconditioned conjugate gradient method is the best tool for efficient solution of large-scale symmetric systems with sparse positive definite matrices. Here, the performance of two preconditioners is studied, namely the Modified Incomplete Cholesky factorization MIC(0) and the Circulant Block-Factorization (CBF) preconditioning. Portable parallel codes are developed based on Message Passing Interface (MPI) standards. The comparative analysis is mostly based on the execution times to run the parallel codes. The number of iterations for both preconditioners are also discussed. The performed numerical tests on parallel computer systems demonstrate the level of efficiency of the developed algorithms. The obtained parallel speed-up and efficiency well illustrate the scope of efficient applications.