Fourier two-level analysis for higher dimensional discontinuous Galerkin discretisation
| Autor: | van Marc Raalte, Piet Hemker |
|---|---|
| Přispěvatelé: | Scientific Computing |
| Jazyk: | angličtina |
| Rok vydání: | 2004 |
| Předmět: |
Numerical analysis
Mathematical analysis General Engineering Theoretical Computer Science Polynomial basis Multigrid method Computational Theory and Mathematics Rate of convergence Discontinuous Galerkin method Modeling and Simulation Convergence (routing) Computer Vision and Pattern Recognition Poisson's equation Software Linear equation Mathematics |
| Zdroj: | Computing and Visualization in Science, 7, 159-172 |
| ISSN: | 1432-9360 |
| Popis: | In this paper we study the convergence of a multigrid method for the solution of a two-dimensional linear second order elliptic equation, discretized by discontinuous Galerkin (DG) methods. For the Baumann---Oden and for the symmetric DG method, we give a detailed analysis of the convergence for cell- and point-wise block-relaxation strategies. We show that, for a suitably constructed two-dimensional polynomial basis, point-wise block partitioning gives much better results than the classical cell-wise partitioning. Independent of the mesh size, for Poisson's equation, simple MG cycles with block-Gauss---Seidel or symmetric block-Gauss---Seidel smoothing, yield a convergence rate of 0.4---0.6 per iteration sweep for both DG-methods studied. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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