Open AccessBlack box multigrid solver for definite and indefinite problems
Author(s) -
Yair Shapira
Publication year - 1997
Language(s) - English
Resource type - Reports
DOI - 10.2172/431140
Subject(s) - multigrid method , solver , separable space , mathematics , black box , grid , computer science , positive definite matrix , mathematical optimization , helmholtz free energy , decomposition method (queueing theory) , helmholtz equation , algorithm , partial differential equation , mathematical analysis , boundary value problem , eigenvalues and eigenvectors , geometry , discrete mathematics , artificial intelligence , physics , quantum mechanics
A two-level analysis method for certain separable problems is introduced. It motivates the definition of improved versions of Black Box Multigrid for diffusion problems with discontinuous coefficients and indefinite Helmholtz equations. For anisotropic problems, it helps in choosing suitable implementations for frequency decomposition multigrid methods. For highly indefinite problems, it provides a way to choose in advance a suitable mesh size for the coarsest grid used. Numerical experiments confirm the analysis and show the advantage of the present methods for several examples