Performance of fully-coupled algebraic multilevel domain decomposition preconditioners for incompressible flow and transport.

Journal Article · Wed Dec 01 04:00:00 EST 2004 · Proposed for publication in International Journal for Numerical Methods in Engineering.

OSTI ID:915194

Shadid, John Nicolas; Lin, Paul Tinphone; Tuminaro, Raymond Stephen ^[1]

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1. Sandia National Laboratories , Livermore, CA

This study investigates algebraic multilevel domain decomposition preconditioners of the Schwarz type for solving linear systems associated with Newton-Krylov methods. The key component of the preconditioner is a coarse approximation based on algebraic multigrid ideas to approximate the global behavior of the linear system. The algebraic multilevel preconditioner is based on an aggressive coarsening graph partitioning of the non-zero block structure of the Jacobian matrix. The scalability of the preconditioner is presented as well as comparisons with a two-level Schwarz preconditioner using a geometric coarse grid operator. These comparisons are obtained on large-scale distributed-memory parallel machines for systems arising from incompressible flow and transport using a stabilized finite element formulation. The results demonstrate the influence of the smoothers and coarse level solvers for a set of 3D example problems. For preconditioners with more than one level, careful attention needs to be given to the balance of robustness and convergence rate for the smoothers and the cost of applying these methods. For properly chosen parameters, the two- and three-level preconditioners are demonstrated to be scalable to 1024 processors.

• Research Organization: Sandia National Laboratories
• Sponsoring Organization: USDOE
• DOE Contract Number: AC04-94AL85000
• OSTI ID: 915194
• Report Number(s): SAND2004-6641J
• Journal Information: Proposed for publication in International Journal for Numerical Methods in Engineering., Journal Name: Proposed for publication in International Journal for Numerical Methods in Engineering.
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
99 GENERAL AND MISCELLANEOUS
APPROXIMATIONS
COMPUTER CALCULATIONS
CONVERGENCE
FLUID FLOW
INCOMPRESSIBLE FLOW
PERFORMANCE