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Spectral Collocation on Triangular Elements

โœ Scribed by Wilhelm Heinrichs

Book ID
102583283
Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
167 KB
Volume
145
Category
Article
ISSN
0021-9991

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โœฆ Synopsis

We consider the Poisson problem on a segment of the unit disc and on triangles. On the segment we transform the Poisson problem by 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.

๐Ÿ“œ SIMILAR VOLUMES

Spectral Schemes on Triangular Elements
Spectral Schemes on Triangular Elements
โœ Wilhelm Heinrichs; Birgit I. Loch ๐Ÿ“‚ Article ๐Ÿ“… 2001 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 193 KB

The Poisson problem with homogeneous Dirichlet boundary conditions is considered on a triangle. The transformation from square to triangle is realized by mapping an edge of the square onto a corner of the triangle. Then standard Chebyshev collocation techniques can be implemented. Numerical experime

Preconditioned Chebyshev collocation met
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This paper analyzes triangular finite elements for the preconditioning of Chebyshev collocation solutions of elliptic boundary value problems. Results are given for scalar model problems and for both Stokes and Navier-Stokes equations.

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โœ J.S. Hesthaven; P.G. Dinesen; J.P. Lynov ๐Ÿ“‚ Article ๐Ÿ“… 1999 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 280 KB

A spectral collocation multi-domain scheme is developed for the accurate and efficient time-domain solution of Maxwell's equations within multi-layered diffractive optical elements. Special attention is being paid to the modeling of out-of-plane waveguide couplers. Emphasis is given to the proper co