An overlapping Schwarz method for spectral element simulation of three-dimensional incompressible flows.
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.
- Research Organization:
- Argonne National Lab., IL (US)
- Sponsoring Organization:
- US Department of Energy (US)
- DOE Contract Number:
- W-31109-ENG-38
- OSTI ID:
- 775252
- Report Number(s):
- ANL/MCS-P730-1098; TRN: AH200110%%172
- Resource Relation:
- Journal Volume: 120; Conference: IMA Workshop on Parallel Solution of Partial Differential Equations, Minneapolis, MN (US), 06/09/1997--06/13/1997; Other Information: PBD: 29 Oct 1998
- Country of Publication:
- United States
- Language:
- English
Similar Records
Overlapping Schwarz for Nonlinear Problems. An Element Agglomeration Nonlinear Additive Schwarz Preconditioned Newton Method for Unstructured Finite Element Problems
Performance of fully-coupled algebraic multilevel domain decomposition preconditioners for incompressible flow and transport.