Frédéric Nataf
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A scalable Domain Decomposition method for Saddle Point problems with GenEO coarse spaces Open
We present an adaptive domain decomposition (DD) preconditioning technique for the solution of saddle point problems with a 2x2 blocks structure. This work utilises the GenEO theory for symmetric positive definite (SPD) problems (Spillane …
Recent advances in domain decomposition methods for large-scale saddle point problems Open
Scalability of parallel solvers for problems with high heterogeneities relies on adaptive coarse spaces built from generalized eigenvalue problems in the subdomains. The corresponding theory is powerful and flexible but the development of …
Recent Advances in Adaptive Coarse Spaces and Availability in Open Source Libraries Open
Scalability of parallel solvers for problems with high heterogeneities relies on adaptive coarse spaces built from generalized eigenvalue problems in the subdomains. The corresponding theory is powerful and flexible but the development of …
Two-level DDM preconditioners for positive Maxwell equations Open
In this paper we develop and analyse domain decomposition methods for linear systems of equations arising from conforming finite element discretisations of positive Maxwell-type equations. Convergence of domain decomposition methods rely h…
Adaptive Domain Decomposition method for Saddle Point problem in Matrix Form Open
We introduce an adaptive element-based domain decomposition (DD) method for\nsolving saddle point problems defined as a block two by two matrix. The\nalgorithm does not require any knowledge of the constrained space. We assume\nthat all su…
Hybrid Discontinuous Galerkin Discretisation and Domain Decomposition Preconditioners for the Stokes Problem Open
Solving 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 …
Numerical Modeling and High-Speed Parallel Computing: New Perspectives on Tomographic Microwave Imaging for Brain Stroke Detection and Monitoring Open
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Hybrid discontinuous Galerkin discretisation and preconditioning of the Stokes problem with non standard boundary conditions Open
Solving the Stokes equation by an optimal domain decomposition method derived algebraically involves the use of non standard interface conditions whose discretisation is not trivial. For this reason the use of approximation methods such as…