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Homogenization and multigrid
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AI
DOI：10.1007/s006070170036.png)
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摘要
En 中文
For elliptic partial differential equations with periodically oscillating coefficients which may have large jumps. we prove robust convergence of a two-grid algorithm using a prolongation motivated by the theory of homogenization. The corresponding Galerkin operator on the coarse grid turns out to be a discretization of a diffusion operator with homogenized coefficients obtained by solving discrete cell problems. This two-grid method is then embedded inside a multi-grid cycle extending over both the fine and the coarse scale.
Keyword:
homogenization
partial differential equations
oscillating coefficients
multilevel methods
multigrid
block smoothers
robustness
