Scharz Preconditioners for Krylov Methods: Theory and Practice

[摘要] Several numerical methods were produced and analyzed. The main thrust of the work relates to inexact Krylov subspace methods for the solution of linear systems of equations arising from the discretization of partial di erential equa- tions. These are iterative methods, i.e., where an approximation is obtained and at each step. Usually, a matrix-vector product is needed at each iteration. In the inexact methods, this product (or the application of a preconditioner) can be done inexactly. Schwarz methods, based on domain decompositions, are excellent preconditioners for thise systems. We contributed towards their under- standing from an algebraic point of view, developed new ones, and studied their performance in the inexact setting. We also worked on combinatorial problems to help de ne the algebraic partition of the domains, with the needed overlap, as well as PDE-constraint optimization using the above-mentioned inexact Krylov subspace methods.

[发布日期] 2013-05-10

[学科分类] 数学（综合）