A domain decomposition method for discontinuous Galerkin discretizations of Helmholtz problems with plane waves and Lagrange multipliers

A domain decomposition method for the Stokes problem using Lagrange multipliers is described. The dual system associated with the Lagrange multipliers is solved based on an iterative procedure using the two-level finite element tearing and interconnecting (FETI) method. Numerical tests are performed by solving the driven cavity problem. An analysis of the number of outer iterations and an evaluation of the cost of the inner iterations are reported. Comparison with the well-known Uzawa algorithm shows a reduction in the floating point operations count of the inner iterations while achieving the same number of outer iterations.

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Topology optimization problem using domain decomposition method based Lagrange multipliers

2020 6th IEEE Congress on Information Science and Technology (CiSt) ◽

10.1109/cist49399.2021.9357322 ◽

2020 ◽

Author(s):

Ouafaa Raibi ◽

Abdelilah Makrizi

Keyword(s):

Topology Optimization ◽

Domain Decomposition ◽

Lagrange Multipliers ◽

Decomposition Method ◽

Optimization Problem ◽

Domain Decomposition Method ◽

Topology Optimization Problem

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

Computational Methods in Applied Mathematics ◽

10.1515/cmam-2018-0005 ◽

2019 ◽

Vol 19 (4) ◽

pp. 703-722 ◽

Cited By ~ 3

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.

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