Laguerre spectral approximation of elliptic problems in exterior domains (Q811224)

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.