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Journal Articles SIAM Journal on Numerical Analysis Year : 2022

On Domain Decomposition Methods with optimized transmission conditions and cross-points

Abstract

We study a mathematical framework for the construction of domain decomposition methods (DDM) for the model Helmholtz equation with high order transmission conditions (TC) and cross-points. A compatibility condition is formulated for cross-points matrices so that the DDM is proved to be convergent under general conditions. The proof is based on a new global energy formulated on the skeleton of the DDM decomposition. It allows to use transmission operators which have a non trivial anti-symmetric part.
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Dates and versions

hal-03230250 , version 1 (19-05-2021)

Identifiers

  • HAL Id : hal-03230250 , version 1

Cite

Bruno Després, Anouk Nicolopoulos, Bertrand Thierry. On Domain Decomposition Methods with optimized transmission conditions and cross-points. SIAM Journal on Numerical Analysis, 2022, 60 (5), pp.2482-2507. ⟨hal-03230250⟩
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