Parallel iterative solution for h and p approximations of the shallow water equations |
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| Institution: | 1. Dipartimento di Ingegneria, Università degli Studi di Palermo, Palermo, Italy;2. Department of Biological and Agricultural Engineering, Texas A&M University, College Station, TX, USA;3. Department of Civil and Environmental Engineering, Princeton University, Princeton, NJ, USA;1. Department of Civil, Geological, and Environmental Engineering, University of Saskatchewan, Saskatoon, Saskatchewan, Canada;2. Department of Irrigation and Hydraulics Engineering, Cairo University, Giza, Egypt;3. Global Institute for Water Security, University of Saskatchewan, Saskatoon, Saskatchewan, Canada |
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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. |
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