Spectral Chebyshev collocation for the poisson and biharmonic equations
Date
2010ISSN
1064-8275Source
SIAM Journal on Scientific ComputingVolume
32Issue
5Pages
2995-3019Google Scholar check
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This paper is concerned with the spectral Chebyshev collocation solution of the Dirichlet problems for the Poisson and biharmonic equations in a square. The collocation schemes are solved at a cost of 2N3 + O(N2 logN) operations using an appropriate set of basis functions, a matrix diagonalization algorithm, and fast Fourier transforms. For the biharmonic problem, the resulting Schur complement system is solved by a preconditioned biconjugate gradient method. An application of the Poisson spectral preconditioner is discussed for the solution of a variable coefficient spectral problem. Numerical results confirm the efficiency of the proposed algorithms and the spectral and polynomial accuracy of the collocation schemes for smooth and singular solutions, respectively. © 2010 Society for Industrial and Applied Mathematics.