The USC Andrew and Erna Viterbi School of Engineering USC Signal and Image Processing Institute USC Ming Hsieh Department of Electrical Engineering University of Southern California

Technical Report USC-SIPI-154

“Multilevel Filtering Preconditioners: Extensions to More General Elliptic Problems”

by Charles H. Tong, Tony F. Chan and C.C. Jay Kuo

December 1990

We briefly review the concept of multilevel filtering (MF) preconditioners applied to second-order self-adjoint elliptic problems. We then show how to effectively apply this concept to other elliptic problems such as the second-order anisotropic problem, Helmholtz equation, convection-diffusion equation, biharmonic equation, equations on locally refined grids and interface operators arising from domain decomposition methods. Numerical results are given to show the effectiveness of the MF preconditioners on these problems.

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