A two-level domain decomposition method with accurate interface conditions for the Helmholtz problem

2015 ◽  
Vol 107 (1) ◽  
pp. 74-90 ◽  
Author(s):  
Ali Vaziri Astaneh ◽  
Murthy N. Guddati
Keyword(s):  
Domain Decomposition ◽  
Decomposition Method ◽  
Domain Decomposition Method ◽  
Interface Conditions ◽  
Helmholtz Problem

A NEW INTERFACE CEMENT EQUILIBRATED MORTAR (NICEM) METHOD WITH ROBIN INTERFACE CONDITIONS: THE P1 FINITE ELEMENT CASE

2013 ◽  
Vol 23 (12) ◽  
pp. 2253-2292 ◽  
Author(s):  
CAROLINE JAPHET ◽  
YVON MADAY ◽  
FREDERIC NATAF
Keyword(s):  
Finite Element ◽  
Error Analysis ◽  
Domain Decomposition ◽  
Decomposition Method ◽  
Domain Decomposition Method ◽  
Numerical Results ◽  
New Method ◽  
Interface Conditions ◽  
Well Posed

We design and analyze a new non-conforming domain decomposition method, named the NICEM method, based on Schwarz-type approaches that allows for the use of Robin interface conditions on non-conforming grids. The method is proven to be well posed. The error analysis is performed in 2D and in 3D for P1 elements. Numerical results in 2D illustrate the new method.

scholarly journals Hybrid Discontinuous Galerkin Discretisation and Domain Decomposition Preconditioners for the Stokes Problem

2019 ◽  
Vol 19 (4) ◽  
pp. 703-722 ◽  
Author(s):  
Gabriel R. Barrenechea ◽  
Michał Bosy ◽  
Victorita Dolean ◽  
Frédéric Nataf ◽  
Pierre-Henri Tournier
Keyword(s):  
Domain Decomposition ◽  
Discontinuous Galerkin ◽  
Numerical Experiments ◽  
Decomposition Method ◽  
Degrees Of Freedom ◽  
Domain Decomposition Method ◽  
Stokes Problem ◽  
Stability And Convergence ◽  
Interface Conditions ◽  
Optimal Domain

AbstractSolving the Stokes equation by an optimal domain decomposition method derived algebraically involves the use of nonstandard interface conditions whose discretisation is not trivial. For this reason the use of approximation methods such as hybrid discontinuous Galerkin appears as an appropriate strategy: on the one hand they provide the best compromise in terms of the number of degrees of freedom in between standard continuous and discontinuous Galerkin methods, and on the other hand the degrees of freedom used in the nonstandard interface conditions are naturally defined at the boundary between elements. In this paper, we introduce the coupling between a well chosen discretisation method (hybrid discontinuous Galerkin) and a novel and efficient domain decomposition method to solve the Stokes system. We present the detailed analysis of the hybrid discontinuous Galerkin method for the Stokes problem with nonstandard boundary conditions. The full stability and convergence analysis of the discretisation method is presented, and the results are corroborated by numerical experiments. In addition, the advantage of the new preconditioners over more classical choices is also supported by numerical experiments.

scholarly journals A non-overlapping domain decomposition method for the exterior Helmholtz problem

1998 ◽  
pp. 42-66 ◽  
Author(s):  
Armel de La Bourdonnaye ◽  
Charbel Farhat ◽  
Antonini Macedo ◽  
Frédéric Magoulès ◽  
François-Xavier Roux
Keyword(s):  
Domain Decomposition ◽  
Decomposition Method ◽  
Domain Decomposition Method ◽  
Helmholtz Problem ◽  
Overlapping Domain Decomposition

scholarly journals A non-overlapping Schwarz domain decomposition method with high-order finite elements for flow acoustics

2020 ◽  
Vol 369 ◽  
pp. 113223
Author(s):  
Alice Lieu ◽  
Philippe Marchner ◽  
Gwénaël Gabard ◽  
Hadrien Bériot ◽  
Xavier Antoine ◽  
...  
Keyword(s):  
Finite Elements ◽  
Domain Decomposition ◽  
Decomposition Method ◽  
Domain Decomposition Method ◽  
High Order ◽  
Overlapping Schwarz
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