Parallel iterative solution for h and p approximations of the shallow water equations
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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.
| 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 |
| DOI | 10.1016/S0309-1708(97)00006-7 |
| Volume | 21 |
| Issue | 5 |
| Year Published | 1998 |
| Language | English |
| Publisher | Elsevier |
| Description | 11 p. |
| First page | 327 |
| Last page | 337 |
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