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