Generalized combined field integral equations for the iterative solution of the three-dimensional Helmholtz equation
ESAIM: M2AN, 41 1 (2007) 147-167
Published online: 2007-04-26
Articles citing this article
The Citing articles tool gives a list of articles citing the current article.
The citing articles come from EDP Sciences database, as well as other publishers participating in CrossRef Cited-by Linking Program. You can set up your personal account to receive an email alert each time this article is cited by a new article (see the menu on the right-hand side of the abstract page).
Cited article:
This article has been cited by the following article(s):
(2025)
https://doi.org/10.2139/ssrn.5167117
Quasi-local and frequency-robust preconditioners for the Helmholtz first-kind integral equations on the disk
Francois Alouges and Martin AversengESAIM: Mathematical Modelling and Numerical Analysis 58 (2) 793 (2024)
https://doi.org/10.1051/m2an/2023105
Iterative On Surface Radiation Conditions for fast and reliable single and multiple scattering analyses of arbitrarily shaped obstacles
Tahsin KhajahComputer Methods in Applied Mechanics and Engineering 420 116715 (2024)
https://doi.org/10.1016/j.cma.2023.116715
Robust boundary integral equations for the solution of elastic scattering problems via Helmholtz decompositions
Víctor Domínguez and Catalin TurcComputers & Mathematics with Applications 175 152 (2024)
https://doi.org/10.1016/j.camwa.2024.09.013
Method of virtual sources using on-surface radiation conditions for the Helmholtz equation
Sebastian Acosta and Tahsin KhajahEngineering Analysis with Boundary Elements 159 342 (2024)
https://doi.org/10.1016/j.enganabound.2023.12.008
An OSRC Preconditioner for the EFIE
Ignacia Fierro-Piccardo and Timo BetckeIEEE Transactions on Antennas and Propagation 71 (4) 3408 (2023)
https://doi.org/10.1109/TAP.2023.3236762
Standard and Phase Reduced Isogeometric On-Surface Radiation Conditions for acoustic scattering analyses
Xavier Antoine and Tahsin KhajahComputer Methods in Applied Mechanics and Engineering 392 114700 (2022)
https://doi.org/10.1016/j.cma.2022.114700
Stable and efficient FEM-BEM coupling with OSRC regularisation for acoustic wave transmission
Elwin van 't WoutJournal of Computational Physics 450 110867 (2022)
https://doi.org/10.1016/j.jcp.2021.110867
High-Frequency Estimates on Boundary Integral Operators for the Helmholtz Exterior Neumann Problem
J. Galkowski, P. Marchand and E. A. SpenceIntegral Equations and Operator Theory 94 (4) (2022)
https://doi.org/10.1007/s00020-022-02715-2
Fast Calculation of Acoustic Field Distribution for Ultrasonic Transducers Using Look-Up Table Method
Ji Wu, Kefeng Tu, Li Liang, Shuaihua Wang, Zi Wang and Guoqiang LvApplied Sciences 12 (17) 8459 (2022)
https://doi.org/10.3390/app12178459
Boundary integral equation methods for the solution of scattering and transmission 2D elastodynamic problems
Víctor Domínguez and Catalin TurcIMA Journal of Applied Mathematics (2022)
https://doi.org/10.1093/imamat/hxac018
Helmholtz equation for a Neumann condition on a curved boundary: spurious resonances
Armand WirginApplicable Analysis 101 (11) 3841 (2022)
https://doi.org/10.1080/00036811.2022.2045971
Applying GMRES to the Helmholtz equation with strong trapping: how does the number of iterations depend on the frequency?
P. Marchand, J. Galkowski, E. A. Spence and A. SpenceAdvances in Computational Mathematics 48 (4) (2022)
https://doi.org/10.1007/s10444-022-09931-9
Frequency-robust preconditioning of boundary integral equations for acoustic transmission
Elwin van 't Wout, Seyyed R. Haqshenas, Pierre Gélat, Timo Betcke and Nader SaffariJournal of Computational Physics 462 111229 (2022)
https://doi.org/10.1016/j.jcp.2022.111229
New preconditioners for the Laplace and Helmholtz integral equations on open curves: analytical framework and numerical results
François Alouges and Martin AversengNumerische Mathematik 148 (2) 255 (2021)
https://doi.org/10.1007/s00211-021-01189-5
Analytical preconditioners for Neumann elastodynamic boundary element methods
Stéphanie Chaillat, Marion Darbas and Frédérique Le LouërPartial Differential Equations and Applications 2 (2) (2021)
https://doi.org/10.1007/s42985-021-00075-x
Local on-surface radiation condition for multiple scattering of waves from convex obstacles
Sebastián AcostaComputer Methods in Applied Mechanics and Engineering 378 113697 (2021)
https://doi.org/10.1016/j.cma.2021.113697
Non Uniform Rational B-Splines and Lagrange approximations for time-harmonic acoustic scattering: accuracy and absorbing boundary conditions
S.M. Dsouza, T. Khajah, X Antoine, S.P.A. Bordas and S. NatarajanMathematical and Computer Modelling of Dynamical Systems 27 (1) 263 (2021)
https://doi.org/10.1080/13873954.2021.1902355
An Introduction to Operator Preconditioning for the Fast Iterative Integral Equation Solution of Time-Harmonic Scattering Problems
Xavier Antoine and Marion DarbasMultiscale Science and Engineering 3 (1) 1 (2021)
https://doi.org/10.1007/s42493-021-00057-6
A fast full-wave solver for calculating ultrasound propagation in the body
S.R. Haqshenas, P. Gélat, E. van ’t Wout, T. Betcke and N. SaffariUltrasonics 110 106240 (2021)
https://doi.org/10.1016/j.ultras.2020.106240
Regularized integral equation methods for elastic scattering problems in three dimensions
Oscar P. Bruno and Tao YinJournal of Computational Physics 410 109350 (2020)
https://doi.org/10.1016/j.jcp.2020.109350
A non-overlapping domain decomposition method with high-order transmission conditions and cross-point treatment for Helmholtz problems
A. Modave, A. Royer, X. Antoine and C. GeuzaineComputer Methods in Applied Mechanics and Engineering 368 113162 (2020)
https://doi.org/10.1016/j.cma.2020.113162
Optimized weak coupling of boundary element and finite element methods for acoustic scattering
B. Caudron, X. Antoine and C. GeuzaineJournal of Computational Physics 421 109737 (2020)
https://doi.org/10.1016/j.jcp.2020.109737
The Boundary Element Method in Acoustics: A Survey
Stephen KirkupApplied Sciences 9 (8) 1642 (2019)
https://doi.org/10.3390/app9081642
B-Spline FEM for Time-Harmonic Acoustic Scattering and Propagation
Tahsin Khajah, Xavier Antoine and Stéphane P. A. BordasJournal of Theoretical and Computational Acoustics 27 (03) 1850059 (2019)
https://doi.org/10.1142/S2591728518500597
Wavenumber-explicit analysis for the Helmholtz h-BEM: error estimates and iteration counts for the Dirichlet problem
Jeffrey Galkowski, Eike H. Müller and Euan A. SpenceNumerische Mathematik 142 (2) 329 (2019)
https://doi.org/10.1007/s00211-019-01032-y
The Wave-Matching Boundary Integral Equation — An energy approach to Galerkin BEM for acoustic wave propagation problems
Jonathan A. Hargreaves and Yiu W. LamWave Motion 87 4 (2019)
https://doi.org/10.1016/j.wavemoti.2018.07.003
A new accurate residual-based a posteriori error indicator for the BEM in 2D-acoustics
Marc Bakry, Sébastien Pernet and Francis CollinoComputers & Mathematics with Applications 73 (12) 2501 (2017)
https://doi.org/10.1016/j.camwa.2017.03.016
High order surface radiation conditions for time-harmonic waves in exterior domains
Sebastián AcostaComputer Methods in Applied Mechanics and Engineering 322 296 (2017)
https://doi.org/10.1016/j.cma.2017.04.032
Modern Solvers for Helmholtz Problems
Timo Betcke, Elwin van ’t Wout and Pierre GélatGeosystems Mathematics, Modern Solvers for Helmholtz Problems 215 (2017)
https://doi.org/10.1007/978-3-319-28832-1_9
Fast iterative boundary element methods for high-frequency scattering problems in 3D elastodynamics
Stéphanie Chaillat, Marion Darbas and Frédérique Le LouërJournal of Computational Physics 341 429 (2017)
https://doi.org/10.1016/j.jcp.2017.04.020
Multitrace/singletrace formulations and Domain Decomposition Methods for the solution of Helmholtz transmission problems for bounded composite scatterers
Carlos Jerez-Hanckes, Carlos Pérez-Arancibia and Catalin TurcJournal of Computational Physics 350 343 (2017)
https://doi.org/10.1016/j.jcp.2017.08.050
Well-conditioned boundary integral equation formulations and Nyström discretizations for the solution of Helmholtz problems with impedance boundary conditions in two-dimensional Lipschitz domains
Catalin Turc, Yassine Boubendir and Mohamed Kamel RiahiJournal of Integral Equations and Applications 29 (3) (2017)
https://doi.org/10.1216/JIE-2017-29-3-441
Asymptotic expansions of the Helmholtz equation solutions using approximations of the Dirichlet to Neumann operator
Souaad Lazergui and Yassine BoubendirJournal of Mathematical Analysis and Applications 456 (2) 767 (2017)
https://doi.org/10.1016/j.jmaa.2017.07.047
Formulation and accuracy of On-Surface Radiation Conditions for acoustic multiple scattering problems
Hasan Alzubaidi, Xavier Antoine and Chokri ChnitiApplied Mathematics and Computation 277 82 (2016)
https://doi.org/10.1016/j.amc.2015.12.023
1321 (2015)
https://doi.org/10.1109/ICEAA.2015.7297331
Integral equations requiring small numbers of Krylov-subspace iterations for two-dimensional smooth penetrable scattering problems
Yassine Boubendir, Oscar Bruno, David Levadoux and Catalin TurcApplied Numerical Mathematics 95 82 (2015)
https://doi.org/10.1016/j.apnum.2015.01.005
Regularized Combined Field Integral Equations for Acoustic Transmission Problems
Yassine Boubendir, Víctor Domínguez, David Levadoux and Catalin TurcSIAM Journal on Applied Mathematics 75 (3) 929 (2015)
https://doi.org/10.1137/140964230
High-order Nyström discretizations for the solution of integral equation formulations of two-dimensional Helmholtz transmission problems
Yassine Boubendir, Catalin Turc and Víctor DomínguezIMA Journal of Numerical Analysis drv010 (2015)
https://doi.org/10.1093/imanum/drv010
μ-diff: An open-source Matlab toolbox for computing multiple scattering problems by disks
Bertrand Thierry, Xavier Antoine, Chokri Chniti and Hasan AlzubaidiComputer Physics Communications 192 348 (2015)
https://doi.org/10.1016/j.cpc.2015.03.013
Directional Preconditioner for 2D High Frequency Obstacle Scattering
Lexing YingMultiscale Modeling & Simulation 13 (3) 829 (2015)
https://doi.org/10.1137/140985135
Well‐conditioned boundary integral formulations for high‐frequency elastic scattering problems in three dimensions
M. Darbas and F. Le LouërMathematical Methods in the Applied Sciences 38 (9) 1705 (2015)
https://doi.org/10.1002/mma.3179
On-surface radiation condition for multiple scattering of waves
Sebastian AcostaComputer Methods in Applied Mechanics and Engineering 283 1296 (2015)
https://doi.org/10.1016/j.cma.2014.08.022
Conforming boundary element methods in acoustics
Pasi Ylä-Oijala, Sami P. Kiminki and Seppo JärvenpääEngineering Analysis with Boundary Elements 50 447 (2015)
https://doi.org/10.1016/j.enganabound.2014.10.002
Approximate local Dirichlet-to-Neumann map for three-dimensional time-harmonic elastic waves
Stéphanie Chaillat, Marion Darbas and Frédérique Le LouërComputer Methods in Applied Mechanics and Engineering 297 62 (2015)
https://doi.org/10.1016/j.cma.2015.08.013
A fast boundary element method for the scattering analysis of high-intensity focused ultrasound
Elwin van 't Wout, Pierre Gélat, Timo Betcke and Simon ArridgeThe Journal of the Acoustical Society of America 138 (5) 2726 (2015)
https://doi.org/10.1121/1.4932166
Well-conditioned boundary integral equation formulations for the solution of high-frequency electromagnetic scattering problems
Yassine Boubendir and Catalin TurcComputers & Mathematics with Applications 67 (10) 1772 (2014)
https://doi.org/10.1016/j.camwa.2014.04.003
Discretization of the Time Domain CFIE for Acoustic Scattering Problems Using Convolution Quadrature
Qiang Chen and Peter MonkSIAM Journal on Mathematical Analysis 46 (5) 3107 (2014)
https://doi.org/10.1137/110833555
A remark on the single scattering preconditioner applied to boundary integral equations
B. ThierryJournal of Mathematical Analysis and Applications 413 (1) 212 (2014)
https://doi.org/10.1016/j.jmaa.2013.11.051
Approximate local magnetic-to-electric surface operators for time-harmonic Maxwell's equations
M. El Bouajaji, X. Antoine and C. GeuzaineJournal of Computational Physics 279 241 (2014)
https://doi.org/10.1016/j.jcp.2014.09.011
A Global Galerkin Method for Solving the Exterior Neumann Problem for the Helmholtz Equation Using Panich's Integral Equation Approach
Andreas Kleefeld and Tzu-Chu LinSIAM Journal on Scientific Computing 35 (3) A1709 (2013)
https://doi.org/10.1137/120873066
Spectral and condition number estimates of the acoustic single-layer operator for low-frequency multiple scattering in dense media
Bertrand Thierry and Xavier AntoineJournal of Computational and Applied Mathematics 239 380 (2013)
https://doi.org/10.1016/j.cam.2012.09.005
Combining analytic preconditioner and Fast Multipole Method for the 3-D Helmholtz equation
M. Darbas, E. Darrigrand and Y. LafrancheJournal of Computational Physics 236 289 (2013)
https://doi.org/10.1016/j.jcp.2012.10.059
Spectral and condition number estimates of the acoustic single-layer operator for low-frequency multiple scattering in dilute media
Xavier Antoine and Bertrand ThierryComputer Methods in Applied Mechanics and Engineering 265 242 (2013)
https://doi.org/10.1016/j.cma.2012.04.017
Well-conditioned boundary integral equations for two- dimensional sound-hard scattering problems in domains with corners
Akash Anand, Jeff Ovall and Catalin TurcJournal of Integral Equations and Applications 24 (3) (2012)
https://doi.org/10.1216/JIE-2012-24-3-321
A quasi-optimal non-overlapping domain decomposition algorithm for the Helmholtz equation
Y. Boubendir, X. Antoine and C. GeuzaineJournal of Computational Physics 231 (2) 262 (2012)
https://doi.org/10.1016/j.jcp.2011.08.007
A well-conditioned integral equation for iterative solution of scattering problems with a variable Leontovitch boundary condition
Sébastien PernetESAIM: Mathematical Modelling and Numerical Analysis 44 (4) 781 (2010)
https://doi.org/10.1051/m2an/2010023
Numerical experiments using CHIEF to treat the nonuniqueness in solving acoustic axisymmetric exterior problems via boundary integral equations
Adel A.K. Mohsen and Martin OchmannJournal of Advanced Research 1 (3) 227 (2010)
https://doi.org/10.1016/j.jare.2010.05.006
Local solutions to high-frequency 2D scattering problems
Andreas Asheim and Daan HuybrechsJournal of Computational Physics 229 (14) 5357 (2010)
https://doi.org/10.1016/j.jcp.2010.03.034
Electromagnetic integral equations requiring small numbers of Krylov-subspace iterations
Oscar Bruno, Tim Elling, Randy Paffenroth and Catalin TurcJournal of Computational Physics 228 (17) 6169 (2009)
https://doi.org/10.1016/j.jcp.2009.05.020
Iterative Solutions for Electromagnetic Fields at Perfectly Reflective and Transmissive Interfaces Using Clifford Algebra and the Multidimensional Cauchy Integral
A. Chantaveerod and A.D. SeagarIEEE Transactions on Antennas and Propagation 57 (11) 3489 (2009)
https://doi.org/10.1109/TAP.2009.2032099
An integral preconditioner for solving the two-dimensional scattering transmission problem using integral equations
X. Antoine and Y. BoubendirInternational Journal of Computer Mathematics 85 (10) 1473 (2008)
https://doi.org/10.1080/00207160802033335