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Efficient spectral-Galerkin methods for polar and cylindrical geometries. (English) Zbl 1180.65160
A new spectral-Galerkin approach for solving the Poisson-type equation in polar geometry is introduced and analyzed. The pole singularity is treated naturally through an appropriate variational formulation. Clustering of collocation points near the pole, a problem common to the spectral-Galerkin algorithms in the literature, is prevented through a change of variable in the radial direction. The method is very efficient and gives spectral accuracy, and can be easily adopted to solve problems in cylindrical geometries and with general boundary conditions. Boundary lifting of general inhomgeneous boundary conditions is also addressed.

##### MSC:
 65N35 Spectral, collocation and related methods for boundary value problems involving PDEs 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
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##### References:
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