Spectral collocation on triangular elements. (English) Zbl 0909.65089
Poisson problems on a segment of the unit disc and on triangles are considered. Using polar coordinates, the triangular elements are mapped on rectangular domains, where standard spectral collocation schemes are available. The authors employs a Chebyshev collocation method with Gauss-Labatto nodes in the polar coordinates. Both for smooth and singular solutions the expected high spectral accuracy is achieved. 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.
Reviewer: Qin Mengzhao (Beijing)
MSC:
| 65N35 | Spectral, collocation and related methods for boundary value problems involving PDEs |
| 65F10 | Iterative numerical methods for linear systems |
| 65F35 | Numerical computation of matrix norms, conditioning, scaling |
| 35J05 | Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation |
| 65N55 | Multigrid methods; domain decomposition for boundary value problems involving PDEs |
Keywords:
spectral collocation method; triangular element; auxiliary mapping; preconditioning; domain decomposition; Chebyshev collocation method; singular solutions; finite difference; iterative solverReferences:
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