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Spectral collocation on triangular elements
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DOI：10.1006/jcph.1998.6052.png)
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Abstract
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We consider the Poisson problem on a segment of the unit disc and on triangles. On the segment we transform the Poisson problem bl, means of polar coordinates. In these new coordinates we have a problem in a rectangle which can easily be mapped onto the square. Here standard Chebyshev collocation techniques can be applied. Then the segment is mapped onto a triangle where the same spectral scheme may be used. By numerical tests we observed the expected high spectral accuracy. Due to the corner singularity a singular behaviour of the solution can be expected. Here we improved the accuracy by auxiliary mapping techniques. Further, it is shown that finite difference preconditioning can be successfully applied in order to construct an efficient iterative solver. Finally, a domain decomposition technique is applied to the patching of a rectangular and a triangular element. (C) 1998 Academic Press.
Keywords:
spectral
collocation
triangles
auxiliary mapping
preconditioning
domain decomposition
Journal
IF:
3.8
Papers:
1.6W
Citations:
7.4W
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