49 citations · 164 across the 24 of their papers we have counts for
27 papers
A Guided Tour of Modern Domain Decomposition: From Schwarz Iterations to Robust Preconditioners and HPC Implementations
Victorita Dolean, Pierre Jolivet, Frédéric Nataf +1
Domain decomposition methods (DDMs) provide a unifying framework for the scalable numerical solution of partial differential equations. Originating from Schwarz's alternating metho…
Achieving wavenumber robustness in domain decomposition for heterogeneous Helmholtz equation: an overview of spectral coarse spaces
Victorita Dolean, Mark Fry, Matthias Langer +2
Solving time-harmonic wave propagation problems in the frequency domain within heterogeneous media poses significant mathematical and computational challenges, particularly in the…
Modal analysis of a domain decomposition method for Maxwell's equations in a waveguide
Victorita Dolean, Antoine Tonnoir, Pierre-Henri Tournier
Time-harmonic wave propagation problems, especially those governed by Maxwell's equations, pose significant computational challenges due to the non-self-adjoint nature of the opera…
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…
Numerical Modeling for Shoulder Injury Detection Using Microwave Imaging
Sahar Borzooei, Pierre-Henri Tournier, Victorita Dolean +4
A portable imaging system for the on-site detection of shoulder injury is necessary to identify its extent and avoid its development to severe condition. Here, firstly a microwave…
A robust and adaptive GenEO-type domain decomposition preconditioner for problems in three-dimensional general topologies
Niall Bootland, Victorita Dolean, Frédéric Nataf +1
In this paper we design, analyse and test domain decomposition methods for linear systems of equations arising from conforming finite element discretisations of positive Maxwell-ty…
Simulation of the 3D Radiative Transfer with Anisotropic Scattering for Convective Trails
Olivier Pironneau, Pierre-Henri Tournier
The integro-differential formulation of the RTE and its solution by iterations on the source has been extended here to handle anisotropic scattering. The iterative part of the meth…
Reflective Conditions for Radiative Transfer in Integral Form with H-Matrices
Olivier Pironneau, Pierre-Henri Tournier
In a recent article the authors showed that the radiative Transfer equations with multiple frequencies and scattering can be formulated as a nonlinear integral system. In the prese…
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…
Numerical assessment of PML transmission conditions in a domain decomposition method for the Helmholtz equation
Niall Bootland, Sahar Borzooei, Victorita Dolean +1
The convergence rate of domain decomposition methods (DDMs) strongly depends on the transmission condition at the interfaces between subdomains. Thus, an important aspect in improv…
Solution of time-harmonic Maxwell's equations by a domain decomposition method based on PML transmission conditions
Sahar Borzooei, Victorita Dolean, Pierre-Henri Tournier +1
Numerical discretization of the large-scale Maxwell's equations leads to an ill-conditioned linear system that is challenging to solve. The key requirement for successive solutions…
Does 3D frequency-domain FWI of full-azimuth/long-offset OBN data feasible? The Gorgon case study
S. Operto, P. Amestoy, H. S. Aghamiry +13
Frequency-domain Full Waveform Inversion (FWI) is potentially amenable to efficient processing of full-azimuth long-offset stationary-recording seabed acquisition carried out with…
A PIC method with Forward-Backward Lagrangian reconstructions
Martin Campos Pinto, Merlin Pelz, Pierre-Henri Tournier
In this work we describe a particle simulation method where the bulk density is periodically remapped on a coarse spline grid using a Forward-Backward Lagrangian (FBL) approac…
Radiative Transfer For Variable 3D Atmospheres
Francois Golse, Frederic Hecht, Olivier Pironneau +2
To study the temperature in a gas subjected to electromagnetic radiations, one may use the Radiative Transfer equations coupled with the Navier-Stokes equations. The problem has 7…
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 comparison of coarse spaces for Helmholtz problems in the high frequency regime
Niall Bootland, Victorita Dolean, Pierre Jolivet +1
Solving time-harmonic wave propagation problems in the frequency domain and within heterogeneous media brings many mathematical and computational challenges, especially in the high…
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…
Large-scale frequency-domain seismic wave modeling on {\it{h}}-adaptive tetrahedral meshes with iterative solver and multi-level domain-decomposition preconditioners
Victorita Dolean, Pierre Jolivet, Stéphane Operto +1
Frequency-domain full-waveform inversion (FWI) is suitable for long-offset stationary-recording acquisition, since reliable subsurface models can be reconstructed with a few freque…
Iterative frequency-domain seismic wave solvers based on multi-level domain-decomposition preconditioners
Victorita Dolean, Pierre Jolivet, Stéphane Operto +1
Frequency-domain full-waveform inversion (FWI) is suitable for long-offset stationary-recording acquisition, since reliable subsurface models can be reconstructed with a few freque…
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…
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…
Domain decomposition preconditioning for the high-frequency time-harmonic Maxwell equations with absorption
Marcella Bonazzoli, Victorita Dolean, Ivan G. Graham +2
This paper rigorously analyses preconditioners for the time-harmonic Maxwell equations with absorption, where the PDE is discretised using curl-conforming finite-element methods of…
A two-level domain-decomposition preconditioner for the time-harmonic Maxwell's equations
Marcella Bonazzoli, Victorita Dolean, Ivan Graham +2
The construction of fast iterative solvers for the indefinite time-harmonic Maxwell's system at mid- to high-frequency is a problem of great current interest. Some of the difficult…