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An additive Schwarz preconditioner for the spectral element ocean model formulation of the shallow water equations. (English) Zbl 1041.68127
Summary: We discretize the shallow water equations with an Adams-Bashford scheme combined with the Crank-Nicholson scheme for the time derivatives and spectral elements for the discretization in space. The resulting coupled system of equations will be reduced to a Schur complement system with a special structure of the Schur complement. This system can he solved with a preconditioned conjugate gradients, where the matrix-vector product is only implicitly given. We derive an overlapping block preconditioner based on additive Schwarz methods for preconditioning the reduced system.

68W10 Parallel algorithms in computer science
65Y05 Parallel numerical computation
47N40 Applications of operator theory in numerical analysis
76D33 Waves for incompressible viscous fluids
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