h-p Spectral Element Method for Elliptic Problems on Non-smooth Domains Using Parallel Computers |
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Authors: | S K Tomar |
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Affiliation: | 1. Johann Radon Inst. for Computational and Applied Mathematics, Austrian Academy of Sciences, Altenbergerstra?e 69, 4040, Linz, Austria
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Abstract: | We propose a new h-p spectral element method to solve elliptic boundary value problems with mixed Neumann and Dirichlet boundary conditions on
non-smooth domains. The method is shown to be exponentially accurate and asymptotically faster than the standard h-p finite element method. The spectral element functions are fully non-conforming for pure Dirichlet problems and conforming
only at the vertices of the elements for mixed problems, and hence, the dimension of the resulting Schur complement matrix is
quite small. The method is a least-squares collocation method and the resulting normal equations are solved using preconditioned conjugate gradient method with an almost optimal preconditioner. The algorithm is suitable for a distributed memory parallel computer. The numerical
results of a number of model problems are presented, which confirm the theoretical estimates. |
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Keywords: | Primary 35J25 65N12 65N35 65Y05 |
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