论文信息 - Spectral multigrid methods for elliptic equations II

Spectral multigrid methods for elliptic equations II

A detailed description of spectral multigrid methods is provided. This includes the interpolation and coarse-grid operators for both periodic and Dirichlet problems. The spectral methods for periodic problems use Fourier series and those for Dirichlet problems are based upon Chebyshev polynomials. An improved preconditioning for Dirichlet problems is given. Numerical examples and practical advice are included.

[1] P. Wesseling,et al. Numerical experiments with a multiple grid and a preconditioned Lanczos type method , 1980 .

[2] R. Nicolaides. On multiple grid and related techniques for solving discrete elliptic systems , 1975 .

[3] Steven A. Orszag,et al. Numerical simulation of incompressible flows within simple boundaries: accuracy , 1971, Journal of Fluid Mechanics.

[4] Dale B. Haidvogel,et al. The Accurate Solution of Poisson's Equation by Expansion in Chebyshev Polynomials , 1979 .

[5] S. Orszag. Spectral methods for problems in complex geometries , 1980 .

[6] M Israeli,et al. Numerical Simulation of Viscous Incompressible Flows , 1974 .

[7] D. Brandt,et al. Multi-level adaptive solutions to boundary-value problems math comptr , 1977 .

[8] J. H. Wilkinson. The algebraic eigenvalue problem , 1966 .

[10] J. Tukey,et al. An algorithm for the machine calculation of complex Fourier series , 1965 .

[11] S. Orszag. Numerical Simulation of Incompressible Flows Within Simple Boundaries. I. Galerkin (Spectral) Representations , 1971 .

[12] L. Richardson. The Approximate Arithmetical Solution by Finite Differences of Physical Problems Involving Differential Equations, with an Application to the Stresses in a Masonry Dam , 1911 .

[13] T. Oliphant. An implicit, numerical method for solving two-dimensional time-dependent diffusion problems , 1961 .

[14] P. Wesseling. Theoretical and Practical Aspects of a Multigrid Method , 1982 .