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Parallel iterative solution for h and p approximations of the shallow water equations

Advances in Water Resources
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Abstract

A p finite element scheme and parallel iterative solver are introduced for a modified form of the shallow water equations. The governing equations are the three-dimensional shallow water equations. After a harmonic decomposition in time and rearrangement, the resulting equations are a complex Helmholz problem for surface elevation, and a complex momentum equation for the horizontal velocity. Both equations are nonlinear and the resulting system is solved using the Picard iteration combined with a preconditioned biconjugate gradient (PBCG) method for the linearized subproblems. A subdomain-based parallel preconditioner is developed which uses incomplete LU factorization with thresholding (ILUT) methods within subdomains, overlapping ILUT factorizations for subdomain boundaries and under-relaxed iteration for the resulting block system. The method builds on techniques successfully applied to linear elements by introducing ordering and condensation techniques to handle uniform p refinement. The combined methods show good performance for a range of p (element order), h (element size), and N (number of processors). Performance and scalability results are presented for a field scale problem where up to 512 processors are used. ?? 1998 Elsevier Science Ltd. All rights reserved.

Additional publication details

Publication type Article
Publication Subtype Journal Article
Title Parallel iterative solution for h and p approximations of the shallow water equations
Series title Advances in Water Resources
Volume 21
Issue 5
Year Published 1998
Language English
Larger Work Type Article
Larger Work Subtype Journal Article
Larger Work Title Advances in Water Resources
First page 327
Last page 337
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