Scalable parallel Newton-Krylov solvers for discontinuous Galerkin discretizations

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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 ... continued below

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Persson, P.-O. December 31, 2008.

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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.

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  • Journal Name: Proc. of the 47th AIAA Aerospace Sciences Meeting and Exhibit

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  • Report No.: LBNL-1427E
  • Grant Number: DE-AC02-05CH11231
  • Office of Scientific & Technical Information Report Number: 946599
  • Archival Resource Key: ark:/67531/metadc901793

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  • December 31, 2008

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  • Sept. 27, 2016, 1:39 a.m.

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  • Nov. 8, 2016, 1:17 p.m.

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Persson, P.-O. Scalable parallel Newton-Krylov solvers for discontinuous Galerkin discretizations, article, December 31, 2008; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc901793/: accessed December 12, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.