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Event Type:

Applied Mathematics and Computation Seminar

Date/Time:

Friday, April 29, 2005 - 05:00

Location:

Gilkey 115

Local Speaker:

Abstract:

Domain decomposition (DD) methods also called multi-domain methods have been first proposed over a century ago. They regained popularity (4113 matches in MathSciNet today) as a divide-and-conquer strategy for numerical solution of partial differential equations and became important for implementation on parallel machines. In the talk I will overview fundamental DD concepts such as Steklov-Poincare operator, Dirichlet-to-Neumann map, alternating Schwarz methods, and Schur complement and will illustrate them on simple examples for the Poisson problem posed on the unit square. Then I will introduce a few modern multi-domain methods applicable to flow and transport models including the mortar formulation which allows to handle non-matching subdomain grids and the heterogeneous multi-domain technique in which different problems are solved in different subdomains.