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International Journal of Computer Mathematics Volume 85, 2008 - Issue 10: INNOVATIVE ALGORITHMS IN SCIENCE AND ENGINEERING
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Original Articles

An integral preconditioner for solving the two-dimensional scattering transmission problem using integral equations

X. Antoine Département de Génie Industriel, Institut National Polytechnique de Lorraine (INPL), Ecole Nationale Supérieure des Mines de Nancy, Nancy, France; Institut Elie Cartan Nancy (IECN), Institut Elie Cartan UMR 7502, Nancy-Université, CNRS, INRIA, Université Henri Poincaré Nancy 1, Vandoeuvre-lès-Nancy, FranceCorrespondence[email protected]
&
Y. Boubendir School of Mathematics, University of Minnesota, S. E. Minneapolis, MN, USA
Pages 1473-1490 | Received 26 May 2006, Accepted 14 Jan 2007, Published online: 01 Sep 2008

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Yin Wang, Jeonghwa Lee & Jun Zhang. (2007) A short survey on preconditioning techniques for large-scale dense complex linear systems in electromagnetics. International Journal of Computer Mathematics 84:8, pages 1211-1223.
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Articles from other publishers (20)

Elwin van 't Wout, Seyyed R. Haqshenas, Pierre Gélat, Timo Betcke & Nader Saffari. (2022) Frequency-robust preconditioning of boundary integral equations for acoustic transmission. Journal of Computational Physics 462, pages 111229.
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Antigoni Kleanthous, Timo Betcke, David P. Hewett, Paul Escapil-Inchauspé, Carlos Jerez-Hanckes & Anthony J. Baran. (2022) Accelerated Calderón preconditioning for Maxwell transmission problems. Journal of Computational Physics 458, pages 111099.
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Stefan D. Search, Christopher D. Cooper & Elwin van't Wout. (2022) Towards optimal boundary integral formulations of the Poisson–Boltzmann equation for molecular electrostatics . Journal of Computational Chemistry 43:10, pages 674-691.
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Elwin van 't Wout, Seyyed R. Haqshenas, Pierre Gélat, Timo Betcke & Nader Saffari. (2022) Boundary integral formulations for acoustic modelling of high-contrast media. Computers & Mathematics with Applications 105, pages 136-149.
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Elwin van 't Wout, Seyyed R. Haqshenas, Pierre Gélat, Timo Betcke & Nader Saffari. (2021) Benchmarking preconditioned boundary integral formulations for acoustics. International Journal for Numerical Methods in Engineering 122:20, pages 5873-5897.
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Xavier Antoine & Marion Darbas. (2021) An Introduction to Operator Preconditioning for the Fast Iterative Integral Equation Solution of Time-Harmonic Scattering Problems. Multiscale Science and Engineering 3:1, pages 1-35.
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S.R. Haqshenas, P. Gélat, E. van ’t Wout, T. Betcke & N. Saffari. (2021) A fast full-wave solver for calculating ultrasound propagation in the body. Ultrasonics 110, pages 106240.
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Carlos Borges & George Biros. (2020) A domain decomposition preconditioning for an inverse volume scattering problem. Inverse Problems 36:3, pages 035016.
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Kirkup. (2019) The Boundary Element Method in Acoustics: A Survey. Applied Sciences 9:8, pages 1642.
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Antigoni Kleanthous, Timo Betcke, David P. Hewett, Matthew W. Scroggs & Anthony J. Baran. (2019) Calderón preconditioning of PMCHWT boundary integral equations for scattering by multiple absorbing dielectric particles. Journal of Quantitative Spectroscopy and Radiative Transfer 224, pages 383-395.
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Víctor Domínguez, Mark Lyon & Catalin Turc. (2016) Well-posed boundary integral equation formulations and Nyström discretizations for the solution of Helmholtz transmission problems in two-dimensional Lipschitz domains. Journal of Integral Equations and Applications 28:3.
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Yassine Boubendir, Oscar Bruno, David Levadoux & Catalin Turc. (2015) Integral equations requiring small numbers of Krylov-subspace iterations for two-dimensional smooth penetrable scattering problems. Applied Numerical Mathematics 95, pages 82-98.
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Yassine Boubendir, Catalin Turc & Víctor Domínguez. (2015) High-order Nyström discretizations for the solution of integral equation formulations of two-dimensional Helmholtz transmission problems. IMA Journal of Numerical Analysis, pages drv010.
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Lexing Ying. (2015) Directional Preconditioner for 2D High Frequency Obstacle Scattering. Multiscale Modeling & Simulation 13:3, pages 829-846.
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Pasi Ylä-Oijala, Sami P. Kiminki & Seppo Järvenpää. (2015) Conforming boundary element methods in acoustics. Engineering Analysis with Boundary Elements 50, pages 447-458.
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Stéphanie Chaillat & Marc Bonnet. (2013) Recent advances on the fast multipole accelerated boundary element method for 3D time-harmonic elastodynamics. Wave Motion 50:7, pages 1090-1104.
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Xavier Claeys & Ralf Hiptmair. (2013) Multi‐Trace Boundary Integral Formulation for Acoustic Scattering by Composite Structures. Communications on Pure and Applied Mathematics 66:8, pages 1163-1201.
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K. Niino & N. Nishimura. (2012) Calderón preconditioning approaches for PMCHWT formulations for Maxwell's equations. International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 25:5-6, pages 558-572.
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Hiroshi Isakari, Kazuki Niino, Hitoshi Yoshikawa & Naoshi Nishimura. (2012) Calderon's preconditioning for periodic fast multipole method for elastodynamics in 3D. International Journal for Numerical Methods in Engineering 90:4, pages 484-505.
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Kazuki Niino & Naoshi Nishimura. (2012) Preconditioning based on Calderon’s formulae for periodic fast multipole methods for Helmholtz’ equation. Journal of Computational Physics 231:1, pages 66-81.
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