Preconditioning Chebyshev Spectral Collocation Method for Elliptic Partial Differential Equations
| Autor: | Sang Dong Kim, Seymour V. Parter |
|---|---|
| Rok vydání: | 1996 |
| Předmět: |
Dirichlet problem
Numerical Analysis Applied Mathematics Mathematical analysis Field (mathematics) Computer Science::Numerical Analysis Mathematics::Numerical Analysis Combinatorics Computational Mathematics Elliptic operator symbols.namesake Elliptic partial differential equation Collocation method Dirichlet boundary condition symbols Computer Science::Data Structures and Algorithms Condition number Eigenvalues and eigenvectors Mathematics |
| Zdroj: | SIAM Journal on Numerical Analysis. 33:2375-2400 |
| ISSN: | 1095-7170 0036-1429 |
| DOI: | 10.1137/s0036142994275998 |
| Popis: | In this paper we analyze a preconditioning technique for the solution of Chebyshev spectral collocation equations with Dirichlet boundary conditions. We obtain bounds on the eigenvalues for the Helmholtz equation. These eigenvalue bounds are obtained as a consequence of estimates on the field of values $(\tilde A_{N^2}U,U)_{l_2}/(\tilde Q_{N^2}U,U)_{l_2}$, where $\tilde A_{N^2}$ is the weighted collocation matrix and $\tilde Q_{N^2}$ is the preconditioner. The preconditioner $\tilde Q_{N^2}$ is robust in the sense that it provides bounds on the $H^1_{0,w}$ condition number of $\tilde Q_{N^2}^{-1}\tilde L_{N^2}$ when $\tilde L_{N^2}$ is the weighted collocation matrix associated with the general elliptic operator $Lu:= -\Delta u + a_1u_x + a_2u_y + a_0u$. |
| Databáze: | OpenAIRE |
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