New Coarse Grid Operators for Highly Oscillatory Coefficient Elliptic Problems

✍ Scribed by Bjorn Engquist; Erding Luo

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 416 KB
• Volume: 129
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1006/jcph.1996.0251

✦ Synopsis

New coarse grid operators are developed for elliptic problems with highly oscillatory coefficients. The new coarse grid operators are constructed directly based on the homogenized differential oper-

ators or hierarchically computed from the finest grid. A detailed description of this construction is provided. Numerical calculations for a two-dimensional elliptic model problem show that the homogwith a j (x, ) strictly positive, continuous, and 1-periodic enized form of the equations is very useful in the design of coarse in each component of . For these equations, there exists grid operators for the multigrid method. A more realistic problem of heat conduction in a composite structure is also considered. ᮊ 1996 a fairly complete analytic theory, known as the homogeni-Academic Press, Inc.

zation theory, such that a rigorous treatment is possible.

The homogenization theory describes the dependence of the large scale features in the solutions from the smaller u ͉ Ѩ⍀ ϭ 0.

DMS91-03104.