Grid Adaptation and Parabolic Equations by Multigrid Techniques.
Final rept. 1 Nov 84-31 Oct 87,
WEIZMANN INST OF SCIENCE REHOVOTH (ISRAEL)
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The long-term goal of our research at the Weizmann Institute is the development of multi-level methods for solving all types of large-scale problems in science and engineering. In addition to an extensive and diverse development of multigrid solvers for differential and integral equations, completely new multilevel approaches have recently been introduced to the areas of large-scale global optimization statistical physics and calculation of many-body interactions see our review. The purpose of our study was to provide criteria for optimizing meshsizes near singularities and to develop fast and flexible multigrid methods for creating the nonuniform grids, their difference equations and their solutions. For simplicity, the Poisson problem was studied, with singularities introduced either in the forcing terms algebraic singularities or sources or in the shape of the boundaries reentrant corners. Local refinements were created by multigrid structures in which some extra finer levels cover increasingly narrower neighborhoods of the singularity, as proposed in another work.
- Theoretical Mathematics