An Energy-Minimizing Approach to Robust Multigrid Methods

Tony F. Chan


We describe a new approach to construct robust interpolation operators for use within multigrid methods, which can handle in a unified fashion problems with problematic (e.g., anisotropic, discontinuous or oscillatory) coefficients, as well as for non-nested unstructured grids. The basic idea derives from recent domain decomposition theory and is based on defining coarse basis functions (from which the interpolation operators can be easily derived) which are {\it stable} (minimize the total energy in a global sense) and have good approximation properties (preserving constants). Numerical results will be presented which show that the resulting multigrid method are very effective.


Joint work with Barry Smith and W. L. Wan.