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A posteriori error analysis for Schwarz overlapping domain decomposition methods | | Jehanzeb Chaudhry
; Don Estep
; Simon Tavener
; | | Date: |
2 Jul 2019 | | Abstract: | Domain decomposition methods are widely used for the numerical solution of
partial differential equations on parallel computers. We develop an
adjoint-based a posteriori error analysis for overlapping multiplicative
Schwarz and for overlapping additive Schwarz domain decomposition methods. In
both cases the numerical error in a user-specified functional of the solution
(quantity of interest), is decomposed into a component that arises as a result
of the finite iteration between the subdomains, and a component that is due to
the spatial discretization. The spatial discretization error can be further
decomposed in to the errors arising on each subdomain. This decomposition of
the total error can then be used as part of a two-stage approach to construct a
solution strategy that efficiently reduces the error in the quantity of
interest. | | Source: | arXiv, 1907.1139 | | Services: | Forum | Review | PDF | Favorites | |
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