PARALLEL PRECONDITIONED KRYLOV SOLVERS for UNSTRUCTURED FINITE ELEMENT REACTING FLOW SOLUTIONS

J.N. Shadid, R. S. Tuminaro, C. H. Tong, K.D. Devine

Sandia National Laboratories

Albuquerque, NM, 87185-1111


Abstract

In this talk we describe a robust iterative linear system solution methodology used for parallel unstructured finite element simulation of strongly coupled fluid flow, heat and mass transfer with non-equilibrium chemical reactions. The linear system solvers are based on preconditioned Krylov subspace methods. Our discussion considers computational efficiency, robustness and some implementation issues related to the proposed preconditioned Krylov solution schemes. The evaluated preconditioners include: i) simple point and block iterative methods, ii) overlapping Schwarz domain decomposition methods with subdomain solvers based on incomplete factorizations, iii) some initial multilevel preconditioners. For this comparison we use a particular spatial discretization of the governing transport-reaction PDEs based on a Galerkin Least Squares (GLS) finite element formulation. Our parallel solution implementation employs automated partitioning algorithms for load balancing unstructured grids, a distributed sparse matrix representation of the global finite element equations, an inexact Newton method and parallel Krylov subspace iterative solvers. We present results for a number of standard 2D CFD benchmark problems and some large 3D reacting flow application problems.

John Shadid

Parallel Computational Sciences Dept. 9221 Mail Stop 1111 PO Box 5800 Sandia National Laboratories Albuquerque, NM 87185

phone: (505) 845 - 7876 fax: (505) 845 - 7442 email: jnshadi@cs.sandia.gov