Chebyshev 3-D spectral and 2-D pseudospectral solvers for the Helmholtz equation. (English) Zbl 0544.65071

Summary: Two Chebyshev solvers are presented for the linear Helmholtz equation. The first algorithm is a 3-D direct spectral solver based on a diagonalization technique, whilst the second performs an iterative pseudospectral 2-D calculation with finite difference preconditioning. Both techniques handle general nonhomogeneous boundary conditions. Computing times and accuracies of the two methods are compared.


65N25 Numerical methods for eigenvalue problems for boundary value problems involving PDEs
65L15 Numerical solution of eigenvalue problems involving ordinary differential equations
34L99 Ordinary differential operators
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35P15 Estimates of eigenvalues in context of PDEs


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