R. A. Walters
E. J. Barragy
1998
<p><span>A </span><i>p</i><span> 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 </span><i>p</i><span> refinement. The combined methods show good performance for a range of </span><i>p</i><span> (element order), </span><i>h</i><span> (element size), and </span><i>N</i><span> (number of processors). Performance and scalability results are presented for a field scale problem where up to 512 processors are used.</span></p>
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10.1016/S0309-1708(97)00006-7
en
Elsevier
Parallel iterative solution for h and p approximations of the shallow water equations
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