An overlapping Schwarz method for spectral element simulation of three-dimensional incompressible flows.

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As the sound speed is infinite for incompressible flows, computation of the pressure constitutes the stiffest component in the time advancement of unsteady simulations. For complex geometries, efficient solution is dependent upon the availability of fast solvers for sparse linear systems. In this paper we develop a Schwarz preconditioner for the spectral element method using overlapping subdomains for the pressure. These local subdomain problems are derived from tensor products of one-dimensional finite element discretizations and admit use of fast diagonalization methods based upon matrix-matrix products. In addition, we use a coarse grid projection operator whose solution is computed via a ... continued below

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22 pages

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Fischer, P. F.; Miller, N. I. & Tufo, H. M. October 29, 1998.

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As the sound speed is infinite for incompressible flows, computation of the pressure constitutes the stiffest component in the time advancement of unsteady simulations. For complex geometries, efficient solution is dependent upon the availability of fast solvers for sparse linear systems. In this paper we develop a Schwarz preconditioner for the spectral element method using overlapping subdomains for the pressure. These local subdomain problems are derived from tensor products of one-dimensional finite element discretizations and admit use of fast diagonalization methods based upon matrix-matrix products. In addition, we use a coarse grid projection operator whose solution is computed via a fast parallel direct solver. The combination of overlapping Schwarz preconditioning and fast coarse grid solver provides as much as a fourfold reduction in simulation time over previously employed methods based upon deflation for parallel solution of multi-million grid point flow problems.

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22 pages

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  • IMA Workshop on Parallel Solution of Partial Differential Equations, Minneapolis, MN (US), 06/09/1997--06/13/1997

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  • Report No.: ANL/MCS-P730-1098
  • Grant Number: W-31109-ENG-38
  • Office of Scientific & Technical Information Report Number: 775252
  • Archival Resource Key: ark:/67531/metadc717753

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  • October 29, 1998

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  • Sept. 29, 2015, 5:31 a.m.

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  • March 23, 2016, 11 a.m.

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Fischer, P. F.; Miller, N. I. & Tufo, H. M. An overlapping Schwarz method for spectral element simulation of three-dimensional incompressible flows., article, October 29, 1998; Illinois. (digital.library.unt.edu/ark:/67531/metadc717753/: accessed January 17, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.