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Finite Difference Preconditioners for Legendre Based Spectral Element Methods on Elliptic Boundary Value Problems
Department of Mathematics, Kyungpook National University, Daegu, South Korea
Computation and Modeling, Shell Technology Center Houston (STCH), Houston, USA
Department of Mathematics, Kyungpook National University, Daegu, South Korea
- 1 Department of Mathematics, Kyungpook National University, Daegu, South Korea
- 2 Computation and Modeling, Shell Technology Center Houston (STCH), Houston, USA
- 3 Department of Mathematics, Kyungpook National University, Daegu, South Korea
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Abstract
Finite difference type preconditioners for spectral element discretizations based on Legendre-Gauss-Lobatto points are analyzed. The latter is employed for the approximation of uniformly elliptic partial differential problems. In this work, it is shown that the condition number of the resulting preconditioned system is bounded independently of both of the polynomial degrees used in the spectral element method and the element sizes. Several numerical tests verify the h-p independence of the proposed preconditioning.
KeywordsFinite Difference PreconditionerIterative MethodSpectral Element MethodElliptic Operator
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