Publication Title | PERFORMANCE OF FULLY-COUPLED DOMAIN DECOMPOSITION PRECONDITIONERS for FINITE ELEMENT TRANSPORT REACTION SIMULATIONS

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Text | PERFORMANCE OF FULLY-COUPLED DOMAIN DECOMPOSITION PRECONDITIONERS for FINITE ELEMENT TRANSPORT REACTION SIMULATIONS | 001 Draft: To be Submitted to JCP DRAFT April 2004 PERFORMANCE OF FULLY-COUPLED DOMAIN DECOMPOSITION PRECONDITIONERS for FINITE ELEMENT TRANSPORT / REACTION SIMULATIONS1 J.N. Shadid2, R. S. Tuminaro2, K.D. Devine2, G.L. Hennigan2, P.T. Lin2 ABSTRACT: In this paper we describe an iterative linear system solution methodology used for parallel unstructured finite element simulation of strongly coupled fluid flow, heat transfer, and mass transfer with non-equilibrium chemical reactions. The nonlinear/linear iterative solution strategies are based on a fully-coupled Newton solver with preconditioned Krylov subspace methods as the underlying linear iteration. Our discussion considers computational efficiency, robustness and a number of practical implementation issues. The evaluated preconditioners are based on additive Schwarz domain decomposition methods which are applicable for totally unstructured meshes. A number of different aspects of Schwarz schemes are considered including subdomain solves, use of overlap and the introduction of a coarse grid solve (a two-level scheme). As we will show, the proper choice among domain decomposition options is often critical to the efficiency of the overall solution scheme. For this comparison we use a particular spatial discretization of the governing transport/reaction partial differential equations (PDEs) based on a stabilized finite element formulation. Results are presented for a number of standard 2D and 3D computational fluid dynamics (CFD) benchmark problems and some large 3D flow, transport and reacting flow application problems. Key Words: Newton-Krylov, fully-coupled solvers, Schwarz Domain Decomposition, two-level methods, multilevel methods, parallel methods, stabilized finite element methods. 1. INTRODUCTION Modern computational fluid dynamics simulations often require the solution of strongly-coupled interacting physics in complex three-dimensional (3D) geometries with high resolution unstructured meshes to capture all the relevant length scales. After suitable spatial discretization and linearization, these simulations can produce large linear systems of equations with on the order 105 to 108 unknowns. As a result efficient and robust parallel iterative solution methods are required to make such simulations tractable for use in analysis or in engineering design cycle times. Preconditioned Krylov iterative methods are among the most robust and fastest iterative solvers over a wide variety of CFD applications [10,21,33,26,38,41]. In the last decade, there has been a significant amount of work on parallel Krylov methods, and a number of general purpose Krylov solver libraries have been developed [11,16,22]. In general, these Krylov methods are relatively straightforward to implement, highly parallel, and are often “optimal” in some sense. While the convergence characteristics of specific Krylov methods remains a topic of research interest, it is now clear that the key factor influencing the robustness and efficiency of these solution methods is preconditioning. The focus of this study is to evaluate several different domain decomposition preconditioner variants for the computational solution of incompressible and low Mach number variable density reacting and non-reacting fluid flows with unstructured mesh finite element methods. These flow problems are characterized by both locally elliptic and nearly hyperbolic behavior, localized steep gradients, and often strongly coupled interactions between the flow velocities, hydrodynamic 1. This work was partially funded by the U.S. Department of Energy’s Mathematical, Information and Computational Sciences Division, and was carried out at Sandia National Laboratories operated for the U.S. Department of Energy under contract no. DE- ACO4-94AL85000. 2. Sandia National Laboratories, Albuquerque, NM, 87185-0316, email for corresponding author: jnshadi@sandia.gov. | Image | PERFORMANCE OF FULLY-COUPLED DOMAIN DECOMPOSITION PRECONDITIONERS for FINITE ELEMENT TRANSPORT REACTION SIMULATIONS |

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