an:01982989
Zbl 1041.68127
Douglas, Craig C.; Haase, Gundolf; Iskandarani, Mohamed
An additive Schwarz preconditioner for the spectral element ocean model formulation of the shallow water equations
EN
ETNA, Electron. Trans. Numer. Anal. 15, 18-28 (2003).
00094088
2003
j
68W10 65Y05 47N40 76D33
shallow water equations; \(h\)-\(p\) finite elements; adaptive grids; multigrid; parallel computing; conjugate gradients; additive Schwarz preconditioner
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.