Name
Abstract | ||
|---|---|---|
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 $2N^3+O(N^2\log N)$ 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. |
Year | DOI | Venue |
|---|---|---|
2010 | 10.1137/100782516 | SIAM J. Scientific Computing |
Keywords | Field | DocType |
poisson spectral preconditioner,dirichlet problem,variable coefficient spectral problem,biharmonic problem,basis function,appropriate set,collocation scheme,biharmonic equation,spectral chebyshev collocation,singular solution,spectral chebyshev collocation solution,biharmonic equations,chebyshev polynomials | Chebyshev polynomials,Mathematical optimization,Dirichlet problem,Mathematical analysis,Orthogonal collocation,Biharmonic equation,Collocation method,Mathematics,Schur complement,Biconjugate gradient method,Collocation | Journal |
Volume | Issue | ISSN |
32 | 5 | 1064-8275 |
Citations | PageRank | References |
1 | 0.38 | 7 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Bernard Bialecki | 1 | 114 | 18.61 |
| Andreas Karageorghis | 2 | 204 | 47.54 |