An additive Schwarz preconditioner for the spectral element ocean model formulation of the shallow water equations

Craig C. Douglas, Gundolf Haase, Mohamed Iskandarani

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

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 be 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.

Original languageEnglish (US)
Pages (from-to)18-28
Number of pages11
JournalElectronic Transactions on Numerical Analysis
Volume15
StatePublished - 2003

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Additive Schwarz
Spectral Elements
Shallow Water Equations
Preconditioner
Ocean
Schur Complement
Formulation
Additive Schwarz Method
Preconditioned Conjugate Gradient
Cross product
Matrix Product
Preconditioning
Coupled System
System of equations
Overlapping
Discretization
Model
Derivative

Keywords

  • Adaptive grids
  • Additive Schwarz preconditioner
  • Conjugate gradients
  • h-p finite elements
  • Multigrid
  • Parallel computing
  • Shallow water equations

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

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AU - Haase, Gundolf

AU - Iskandarani, Mohamed

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N2 - 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 be 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.

AB - 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 be 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.

KW - Adaptive grids

KW - Additive Schwarz preconditioner

KW - Conjugate gradients

KW - h-p finite elements

KW - Multigrid

KW - Parallel computing

KW - Shallow water equations

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