Coulaud, Olivier; Funaro, Daniele; Kavian, Otared Laguerre spectral approximation of elliptic problems in exterior domains. (English) Zbl 0734.73090 Comput. Methods Appl. Mech. Eng. 80, No. 1-3, 451-458 (1990). 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 \(D=\{x\in {\mathbb{R}}^ 2:| x| >1\}\). 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 \(Q=]-1,1[^ 2\). Here domain decomposition techniques are highly recommended. Reviewer: W.Heinrichs Cited in 1 ReviewCited in 47 Documents MSC: 74S30 Other numerical methods in solid mechanics (MSC2010) 65N35 Spectral, collocation and related methods for boundary value problems involving PDEs 65D05 Numerical interpolation Keywords:spectral methods; pseudospectral methods; collocation; Helmholtz equation; domain decomposition PDF BibTeX XML Cite \textit{O. Coulaud} et al., Comput. Methods Appl. Mech. Eng. 80, No. 1--3, 451--458 (1990; Zbl 0734.73090) Full Text: DOI OpenURL References: [1] D. Funaro and O. Kavian, Approximation of some diffusion evolution equations in unbounded domains by Hermite functions, Math. Comp., submitted. · Zbl 0764.35007 [2] Maday, Y.; Pernaud-Thomas, B.; Vandeven, H., Une réhabilitation des méthodes de type Laguerre, Rech. Aérospat., 6, 353-375, (1985) · Zbl 0604.42026 [3] C. Mavriplis, Laguerre polynomials for infinite-domain spectral elements, J. Comput. Physics, to appear. · Zbl 0665.65066 [4] Szego, G., Orthogonal polynomials, (1959), Amer. Mathematical Soc New York · JFM 65.0278.03 [5] Gatteschi, L., Proprietà asintotiche di una funzione associata ai polinomi di Laguerre e loro utilizzazione al calcolo numerico degli zeri dei polinomi stessi, Atti Della academia delle scienze di Torino, Vol. 98, (1963-1964) · Zbl 0131.07102 [6] O. Coulaud, D. Funaro and O. Kavian, in preparation. [7] Funaro, D.; Quarteroni, A.; Zanolli, P., An iterative procedure with interface relaxation for domain decomposition methods, SIAM J. numer. anal., 25, 6, 1213-1236, (1988) · Zbl 0678.65082 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.