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Zbl 0734.73090
Coulaud, Olivier; Funaro, Daniele; Kavian, Otared
Laguerre spectral approximation of elliptic problems in exterior domains.
(English)
[J] Comput. Methods Appl. Mech. Eng. 80, No.1-3, 451-458 (1990). ISSN 0045-7825

Elliptic problems in exterior domains are solved by spectral methods based on expansion by Hermite or Laguerre functions, i.e., Hermite or Laguerre functions multiplied by a decaying exponential. For pseudospectral methods, collocation is imposed at the zeros of these functions. The Helmholtz equation is considered in a domain D. In the first problem we have $D=\{x\in {\bbfR}\sp 2:\vert x\vert >1\}$. Using polar coordinates, the angular variable is approximated by Fourier series, while Laguerre expansion is used for the radial variable. The second problem is defined on the exterior of the square $Q=]-1,1[\sp 2$. Here domain decomposition techniques are highly recommended.
[W.Heinrichs]
MSC 2000:
*74S30 Other numerical methods
65N35 Collocation methods (BVP of PDE)
65D05 Interpolation (numerical methods)

Keywords: spectral methods; pseudospectral methods; collocation; Helmholtz equation; domain decomposition

Cited in: Zbl 0744.73005

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