Journal of the Korean Society for Industrial and Applied Mathematics

  • 제13권4호
  • /
  • Pages.267-280
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  • 2009
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  • 1226-9433(pISSN)
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  • 1229-0645(eISSN)
한국산업응용수학회 (Korean Society for Industrial and Applied Mathematics)
권호 표지

EXPLICIT BOUNDS FOR THE TWO-LEVEL PRECONDITIONER OF THE P1 DISCONTINUOUS GALERKIN METHOD ON RECTANGULAR MESHES

  • 투고 : 2009.09.04
  • 심사 : 2009.11.11
  • 발행 : 2009.12.25
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초록

In this paper we investigate a simple two-level additive Schwarz preconditioner for the P1 symmetric interior penalty Galerkin method of the Poisson equation on rectangular meshes. The construction is based on the decomposition of the global space of piecewise linear polynomials into the sum of local subspaces, each of which corresponds to an element of the underlying mesh, and the global coarse subspace consisting of piecewise constants. This preconditioner is a direct combination of the block Jacobi iteration and the cell-centered finite difference method, and thus very easy to implement. Explicit upper and lower bounds for the maximum and minimum eigenvalues of the preconditioned matrix system are derived and confirmed by some numerical experiments.

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참고문헌

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