54 citations · 139 across the 17 of their papers we have counts for
17 papers · 1 filter
A Robust Two-Level Schwarz Preconditioner For Sparse Matrices
Hussam Al Daas, Pierre Jolivet, Frédéric Nataf +1
This paper introduces a fully algebraic two-level additive Schwarz preconditioner for general sparse large-scale matrices. The preconditioner is analyzed for symmetric positive def…
How does the partition of unity influence SORAS preconditioner?
Marcella Bonazzoli, Xavier Claeys, Frédéric Nataf +1
We investigate the influence of the choice of the partition of unity on the convergence of the Symmetrized Optimized Restricted Additive Schwarz (SORAS) preconditioner for the reac…
Several ways to achieve robustness when solving wave propagation problems
Niall Bootland, Victorita Dolean, Pierre Jolivet +3
Wave propagation problems are notoriously difficult to solve. Time-harmonic problems are especially challenging in mid and high frequency regimes. The main reason is the oscillator…
Two-level DDM preconditioners for positive Maxwell equations
Niall Bootland, Victorita Dolean, Frédéric Nataf +1
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 eq…
A Unified Framework for Double Sweep Methods for the Helmholtz Equation
Nacime Bouziani, Frédéric Nataf, Pierre-Henri Tournier
We consider sweeping domain decomposition preconditioners to solve the Helmholtz equation in the case of stripwise domain decomposition with or without overlaps. We unify their der…
Analysis of the SORAS domain decomposition preconditioner for non-self-adjoint or indefinite problems
Marcella Bonazzoli, Xavier Claeys, Frédéric Nataf +1
We analyze the convergence of the one-level overlapping domain decomposition preconditioner SORAS (Symmetrized Optimized Restricted Additive Schwarz) applied to a generic linear sy…
Mathematical Analysis of Robustness of Two-Level Domain Decomposition Methods with respect to Inexact Coarse Solves
Frédéric Nataf
Convergence of domain decomposition methods rely heavily on the efficiency of the coarse space used in the second level. The GenEO coarse space has been shown to lead to a fully ro…
Parallel Controllability Methods For the Helmholtz Equation
Marcus J. Grote, Frédéric Nataf, Jet Hoe Tang +1
The Helmholtz equation is notoriously difficult to solve with standard numerical methods, increasingly so, in fact, at higher frequencies. Controllability methods instead transform…
Hybrid discontinuous Galerkin discretisation and domain decomposition preconditioners for the Stokes problem
Gabriel R. Barrenechea, Michał Bosy, Victorita Dolean +2
Solving the Stokes equation by an optimal domain decomposition method derived algebraically involves the use of non standard interface conditions whose discretisation is not trivia…
Robin Schwarz algorithm for the NICEM Method: the Pq finite element case
Caroline Japhet, Yvon Maday, Frédéric Nataf
In Gander et al. [2004] we proposed a new non-conforming domain decomposition paradigm, the New Interface Cement Equilibrated Mortar (NICEM) method, based on Schwarz type methods t…
Generalized Filtering Decomposition
Laura Grigori, Frédéric Nataf
This paper introduces a new preconditioning technique that is suitable for matrices arising from the discretization of a system of PDEs on unstructured grids. The preconditioner sa…
Local time steps for a finite volume scheme
Isabelle Faille, Frédéric Nataf, Françoise Willien +1
We present a strategy for solving time-dependent problems on grids with local refinements in time using different time steps in different regions of space. We discuss and analyze t…
A new Cement to Glue non-conforming Grids with Robin interface conditions: the finite element case
Caroline Japhet, Yvon Maday, Frédéric Nataf
We design and analyze a new non-conforming domain decomposition method based on Schwarz type approaches that allows for the use of Robin interface conditions on non-conforming grid…
Simulation of Laser Propagation in a Plasma with a Frequency Wave Equation
Sylvain Desroziers, Frédéric Nataf, Remi Sentis
The aim of this work is to perform numerical simulations of the propagation of a laser in a plasma. At each time step, one has to solve a Helmholtz equation in a domain which consi…
New constructions of domain decomposition methods for systems of PDEs
Victorita Dolean, Frédéric Nataf, Gerd Rapin
We propose new domain decomposition methods for systems of partial differential equations in two and three dimensions. The algorithms are derived with the help of the Smith factori…
A New Domain Decomposition Method for the Compressible Euler Equations
Victorita Dolean, Frédéric Nataf
In this work we design a new domain decomposition method for the Euler equations in 2 dimensions. The basis is the equivalence via the Smith factorization with a third order scalar…
A new construction of perfectly matched layers for the linearized Euler equations
Frédéric Nataf
Based on a PML for the advective wave equation, we propose two PML models for the linearized Euler equations. The derivation of the first model can be applied to other physical mod…