Scalable parallel Newton-Krylov solvers for discontinuous Galerkin discretizations

Journal Article · Wed Dec 31 04:00:00 EST 2008 · Proc. of the 47th AIAA Aerospace Sciences Meeting and Exhibit

OSTI ID:946599

Persson, P -O

We present techniques for implicit solution of discontinuous Galerkin discretizations of the Navier-Stokes equations on parallel computers. While a block-Jacobi method is simple and straight-forward to parallelize, its convergence properties are poor except for simple problems. Therefore, we consider Newton-GMRES methods preconditioned with block-incomplete LU factorizations, with optimized element orderings based on a minimum discarded fill (MDF) approach. We discuss the difficulties with the parallelization of these methods, but also show that with a simple domain decomposition approach, most of the advantages of the block-ILU over the block-Jacobi preconditioner are still retained. The convergence is further improved by incorporating the matrix connectivities into the mesh partitioning process, which aims at minimizing the errors introduced from separating the partitions. We demonstrate the performance of the schemes for realistic two- and three-dimensional flow problems.

• Research Organization: Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, CA (US)
• Sponsoring Organization: Computational Research Division
• DOE Contract Number: AC02-05CH11231
• OSTI ID: 946599
• Report Number(s): LBNL-1427E
• Journal Information: Proc. of the 47th AIAA Aerospace Sciences Meeting and Exhibit, Journal Name: Proc. of the 47th AIAA Aerospace Sciences Meeting and Exhibit
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
COMPUTERS
CONVERGENCE
NAVIER-STOKES EQUATIONS
PERFORMANCE