Colóquio de Matemática, 29 de outubro de 2021, 14:00h

26/10/2021 21:32

Próximo Colóquio

29 de Outubro de 2021, 14:00h

Prof. Dr. Marcus Sarkis-Martins

(Worcester Polytechnic Institute)

 

Introduction to Domain Decomposition Methods

Abstract: Domain Decomposition Method (DDM here refers to the

splitting of a partial differential equation, or its discretization,

into coupled problems on smaller subdomains forming a partition of

the original domain. In a practical application, finite element or other

discretization reduces the problem to the solution of an often huge

algebraic system of equations. Solving this system via factorization

might not be a viable option and basic iterative methods such as the

conjugated gradient method might result

in very slow convergence. The basic idea of DDMs is that instead of solving

one huge problem on a domain, it may be convenient (or necessary) to solve

many smaller problems on single subdomains a certain number of times.

Much of the work on DDM relates to the selection of subproblems that

ensure that the rate of convergence of these iterative methods are fast.

In this talk, I will concentrate on basic ideas on DDMs introduced first

by Hermann Amandus Schwarz in 1870 until becoming a very active area due

to the advent of parallel and distributed computers.

 

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