1,847 research outputs found
Asynchronous global-local non-invasive coupling for linear elliptic problems
This paper presents the first asynchronous version of the Global/Local
non-invasive coupling, capable of dealing efficiently with multiple, possibly
adjacent, patches. We give a new interpretation of the coupling in terms of
primal domain decomposition method, and we prove the convergence of the relaxed
asynchronous iteration. The asynchronous paradigm lifts many bottlenecks of the
Global/Local coupling performance. We illustrate the method on several linear
elliptic problems as encountered in thermal and elasticity studies
A rapidly converging domain decomposition method for the Helmholtz equation
A new domain decomposition method is introduced for the heterogeneous 2-D and
3-D Helmholtz equations. Transmission conditions based on the perfectly matched
layer (PML) are derived that avoid artificial reflections and match incoming
and outgoing waves at the subdomain interfaces. We focus on a subdivision of
the rectangular domain into many thin subdomains along one of the axes, in
combination with a certain ordering for solving the subdomain problems and a
GMRES outer iteration. When combined with multifrontal methods, the solver has
near-linear cost in examples, due to very small iteration numbers that are
essentially independent of problem size and number of subdomains. It is to our
knowledge only the second method with this property next to the moving PML
sweeping method.Comment: 16 pages, 3 figures, 6 tables - v2 accepted for publication in the
Journal of Computational Physic
Scharz Preconditioners for Krylov Methods: Theory and Practice
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#11;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#12;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
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