Multigrid and Krylov Solvers for Large Scale Finite Element Groundwater Flow Simulations on Distributed Memory Parallel Platforms

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In this report we present parallel solvers for large linear systems arising from the finite-element discretization of the three-dimensional steady-state groundwater flow problem. Our solvers are based on multigrid and Krylov subspace methods. The parallel implementation is based on a domain decomposition strategy with explicit message passing using NX and MPI libraries. We have tested our parallel implementations on the Intel Paragon XP/S 150 supercomputer using up to 1024 parallel processors and on other parallel platforms such as SGI/Power Challenge Array, Cray/SGI Origin 2000, Convex Exemplar SPP-1200, and IBM SP using up to 64 processors. We show that multigrid can ... continued below

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26 pages

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Mahinthakumar, K. January 1, 1997.

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Description

In this report we present parallel solvers for large linear systems arising from the finite-element discretization of the three-dimensional steady-state groundwater flow problem. Our solvers are based on multigrid and Krylov subspace methods. The parallel implementation is based on a domain decomposition strategy with explicit message passing using NX and MPI libraries. We have tested our parallel implementations on the Intel Paragon XP/S 150 supercomputer using up to 1024 parallel processors and on other parallel platforms such as SGI/Power Challenge Array, Cray/SGI Origin 2000, Convex Exemplar SPP-1200, and IBM SP using up to 64 processors. We show that multigrid can be a scalable algorithm on distributed memory machines. We demonstrate the effectiveness of parallel multigrid based solvers by solving problems requiring more than 70 million nodes in less than a minute. This is more than 25 times faster than the diagonal preconditioned conjugate gradient method which is one of the more popular methods for large sparse linear systems. Our results also show that multigrid as a stand alone solver works best for problems with smooth coefficients, but for rough coefficients it is best used as a preconditioner for a Krylov subspace method such as the conjugate gradient method. We show that even for extremely heterogeneous systems the multigrid pre-conditioned conjugate gradient method is at least 10 times faster than the diagonally preconditioned conjugate gradient method.

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26 pages

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  • Other Information: PBD: 1 Jan 1997

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  • Report No.: ORNL/TM-13441
  • Grant Number: AC05-00OR22725
  • DOI: 10.2172/814802 | External Link
  • Office of Scientific & Technical Information Report Number: 814802
  • Archival Resource Key: ark:/67531/metadc736801

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Reports, articles and other documents harvested from the Office of Scientific and Technical Information.

Office of Scientific and Technical Information (OSTI) is the Department of Energy (DOE) office that collects, preserves, and disseminates DOE-sponsored research and development (R&D) results that are the outcomes of R&D projects or other funded activities at DOE labs and facilities nationwide and grantees at universities and other institutions.

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  • January 1, 1997

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  • Oct. 18, 2015, 6:40 p.m.

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  • March 31, 2016, 1:21 p.m.

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Mahinthakumar, K. Multigrid and Krylov Solvers for Large Scale Finite Element Groundwater Flow Simulations on Distributed Memory Parallel Platforms, report, January 1, 1997; United States. (digital.library.unt.edu/ark:/67531/metadc736801/: accessed November 24, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.