Some Geometric and Algebraic Aspects of Domain Decomposition Methods

摘要

Our preliminary numerical results show that the DDMs considered have reasonable efficiency. However, there are too many approaches needing systematic experimental investigation to construct high-performance code. This concerns, in particular, the application of various optimized Schwarz methods with different values of parameter θ and coarse grid correction for overlapping or non-overlapping DDM. Of course, the problem of creating an adapted environment for robust SLAE solvers on modern supercomputers requires coordinated efforts of algebraists and programmers.