This paper gives an overview for the method of subspace corrections. The method is first motivated by a discussion on the local behavior of high-frequency components in a solution to an elliptic problem. A simple domain decomposition method is discussed as an illustrative example and multigrid methods are discussed in more detail. Brief discussion are also given to some non-linear examples including eigenvalue problems, obstacle problems and liquid crystal modelings. The relationship between the method of subspace correction and the method of alternating projects is observed and discussed.
All Science Journal Classification (ASJC) codes
- Computational Mathematics
- Applied Mathematics