Open Access
Issue |
ESAIM: M2AN
Volume 57, Number 4, July-August 2023
|
|
---|---|---|
Page(s) | 2451 - 2491 | |
DOI | https://doi.org/10.1051/m2an/2023060 | |
Published online | 27 July 2023 |
- S. Abarbanel and D. Gottlieb, A mathematical analysis of the PML method. J. Comput. Phys. 134 (1997) 357–363. [CrossRef] [MathSciNet] [Google Scholar]
- S. Abarbanel, D. Gottlieb and J.S. Hesthaven, Well-posed perfectly matched layers for advective acoustics. J. Comput. Phys. 154 (1999) 266–283. [CrossRef] [MathSciNet] [Google Scholar]
- S. Abarbanel, D. Gottlieb and J.S. Hesthaven, Long time behavior of the perfectly matched layer equations in computational elactromagnetics, J. Sci. Comput. 17 (2002) 405–422. [CrossRef] [MathSciNet] [Google Scholar]
- D. Appelö, T. Hagstrom and G. Kreiss, Perfectly matched layers for hyperbolic systems: general formulation, well-posedness, and stability. SIAM J. Appl. Math. 67 (2006) 1–23. [CrossRef] [MathSciNet] [Google Scholar]
- S. Asvadurov, V. Druskin, M.N. Guddati and L. Knizhnerman, On optimal finite-difference approximation of PML. SIAM J. Numer. Anal. 41 (2003) 287–305. [CrossRef] [MathSciNet] [Google Scholar]
- N. Baara, J. Diaz and M. Tlemcani, Time domain analysis and localization of a non-local PML for dispersive wave equations. J. Comput. Phys. 445 (2021) 18. [Google Scholar]
- D.H. Baffet, M.J. Grote, S. Imperiale and M. Kachanovska, Energy decay and stability of a perfectly matched layer for the wave equation. J. Sci. Comput. 81 (2019) 2237–2270. [CrossRef] [MathSciNet] [Google Scholar]
- J.-P. Berenger, A perfectly matched layer for the absorption of electromagnetic waves. J. Comput. Phys. 114 (1994) 185–200. [CrossRef] [Google Scholar]
- J.-P. Berenger, Three-dimensional perfectly matched layer for the absorption of electromagnetic waves. J. Comput. Phys. 127 (1996) 363–379. [NASA ADS] [CrossRef] [Google Scholar]
- J.P. Berenger, Improved PML for the FDTD solution of wave-structure interaction problems. IEEE Trans. Antennas Propag. 45 (1997) 466–473. [CrossRef] [Google Scholar]
- E. Bécache and P. Joly, On the analysis of Bérenger’s perfectly matched layers for Maxwell’s equations. M2AN Math. Model. Numer. Anal. 36 (2002) 87–119. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
- E. Bécache and M. Kachanovska, Stable perfectly matched layers for a class of anisotropic dispersive models. Part I: necessary and sufficient conditions of stability. ESAIM Math. Model. Numer. Anal. 51 (2017) 2399–2434. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
- E. Bécache and M. Kachanovska, Stability and convergence analysis of time-domain perfectly matched layers for the wave equation in waveguides. SIAM J. Numer. Anal. 59 (2021) 2004–2039. [CrossRef] [MathSciNet] [Google Scholar]
- E. Bécache, S. Fauqueux and P. Joly, Stability of perfectly matched layers, group velocities and anisotropic waves. J. Comput. Phys. 188 (2003) 399–433. [CrossRef] [MathSciNet] [Google Scholar]
- E. Bécache, P. Petropoulos and S. Gedney, On the long-time behavior of unsplit perfectly matched layers. IEEE Trans. Antennas Propag. 52 (2004) 1335–1342. [CrossRef] [Google Scholar]
- E. Bécache, P. Joly and M. Kachanovska, Stable perfectly matched layers for a cold plasma in a strong background magnetic field. J. Comput. Phys. 341 (2017) 76–101. [CrossRef] [MathSciNet] [Google Scholar]
- E. Bécache, P. Joly and V. Vinoles, On the analysis of perfectly matched layers for a class of dispersive media and application to negative index metamaterials. Math. Comput. 87 (2018) 2775–2810. [CrossRef] [Google Scholar]
- A.S. Bonnet-Ben Dhia, P. Ciarlet Jr. and C.M. Zwölf, Time harmonic wave diffraction problems in materials with sign-shifting coefficients. J. Comput. Appl. Math. 234 (2010) 1912–1919. [CrossRef] [MathSciNet] [Google Scholar]
- M. Cassier, P. Joly and M. Kachanovska, Mathematical models for dispersive electromagnetic waves: an overview. Comput. Math. Appl. 74 (2017) 2792–2830. [Google Scholar]
- A. Chern, A reflectionless discrete perfectly matched layer. J. Comput. Phys. 381 (2019) 91–109. [CrossRef] [MathSciNet] [Google Scholar]
- K.S. Cole and R.H. Cole, Dispersion and absorption in dielectrics I. Alternating current characteristics. J. Chem. Phys. 9 (1941) 341–351. [Google Scholar]
- F. Collino, Perfectly matched absorbing layers for the paraxial equations. J. Comput. Phys. 131 (1997) 164–180. [CrossRef] [MathSciNet] [Google Scholar]
- F. Collino and P.B. Monk, Optimizing the perfectly matched layer. Comput. Methods Appl. Mech. Eng. 164 (1998) 157–171. [CrossRef] [Google Scholar]
- F. Collino and C. Tsogka, Application of the pml absorbing layer model to the linear elastodynamic problem in anisotropic heteregeneous media. Geophysics 66 (2001) 294–307. [CrossRef] [Google Scholar]
- T.J. Cui, D.R. Smith and R. Liu, Metamaterials: Theory, Design, and Applications. Springer (2010). [CrossRef] [Google Scholar]
- S.A. Cummer, Perfectly matched layer behavior in negative refractive index materials. IEEE Antennas Wirel. Propag. Lett. 3 (2004) 172–175. [CrossRef] [Google Scholar]
- E. Demaldent and S. Imperiale, Perfectly matched transmission problem with absorbing layers: application to anisotropic acoustics in convex polygonal domains. Int. J. Numer. Methods Eng. 96 (2013) 689–711. [CrossRef] [Google Scholar]
- J. Diaz and P. Joly, A time domain analysis of PML models in acoustics. Comput. Methods Appl. Mech. Eng. 195 (2006) 3820–3853. [CrossRef] [Google Scholar]
- K. Duru and G. Kreiss, On the accuracy and stability of the perfectly matched layer in transient waveguides. J. Sci. Comput. 53 (2012) 642–671. [CrossRef] [MathSciNet] [Google Scholar]
- S.D. Gedney, An anisotropic perfectly matched layer-absorbing medium for the truncation of fdtd lattices. IEEE Trans. Antennas Propag. 44 (1996) 1630–1639. [CrossRef] [Google Scholar]
- S. Havriliak and S. Negami, A complex plane representation of dielectric and mechanical relaxation processes in some polymers. Polymer 8 (1967) 161–210. [Google Scholar]
- L. Halpern, S. Petit-Bergez and J. Rauch, The analysis of matched layers. Conflu. Math. 3 (2011) 159–236. [CrossRef] [Google Scholar]
- F. Hastings, J.B. Schneider and S.L. Broschat, Application of the perfectly matched layer (PML) absorbing boundary condition to elastic wave propagation. J. Acoust. Soc. Am. 100 (1996) 3061–3069. [CrossRef] [Google Scholar]
- J.S. Hesthaven, On the Analysis and construction of perfectly matched layers for the linearized Euler equations. J. Comput. Phys. 142 (1998) 129–147. [CrossRef] [MathSciNet] [Google Scholar]
- F.Q. Hu, On absorbing boundary conditions for linearized euler equations by a perfectly matched layer. J. Comput. Phys. 129 (1996) 201–219. [NASA ADS] [CrossRef] [Google Scholar]
- F.Q. Hu, A stable, perfectly matched layer for linearized Euler equations in unsplit physical variables. J. Comput. Phys. 173 (2001) 455–480. [NASA ADS] [CrossRef] [Google Scholar]
- Y. Huang, H. Jia and J. Li, Analysis and application of an equivalent Berenger’s PML model. J. Comput. Appl. Math. 333 (2018) 157–169. [CrossRef] [MathSciNet] [Google Scholar]
- A. Modave, E. Delhez and C. Geuzaine, Optimizing perfectly matched layers in discrete contexts. Int. J. Numer. Methods Eng. 99 (2014) 410–437. [CrossRef] [Google Scholar]
- F. Nataf, A new approach to perfectly matched layers for the linearized Euler system. J. Comput. Phys. 214 (2006) 757–772. [CrossRef] [MathSciNet] [Google Scholar]
- J.M. Ortega, Numerical analysis, in Classics in Applied Mathematics. Vol. 3, second edition, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA (1990). [Google Scholar]
- P.G. Petropoulos, Reflectionless sponge layers as absorbing boundary condition for the numerical solution of Maxwell’s equations in rectangular, cylindrical, and spherical coordinates. SIAM J. Appl. Math. 60 (2000) 1037–1058. [CrossRef] [MathSciNet] [Google Scholar]
- P.G. Petropoulos, L. Zhao and A.C. Cangellaris, A reflectionless sponge layer absorbing boundary condition for the solution of Maxwell’s equations with high-order staggered finite difference schemes. J. Comput. Phys. 139 (1998) 184–208. [CrossRef] [MathSciNet] [Google Scholar]
- F.-J. Sayas, Retarded potentials and time domain boundary integral equations, in Springer Series in Computational Mathematics. Vol. 50, Springer, Cham (2016). [CrossRef] [Google Scholar]
- J. Schöberl, Netgen – an advancing front 2d/3d-mesh generator based on abstract rules. Comput. Visual. Sci. 1 (1997) 41–52. [CrossRef] [Google Scholar]
- J. Schöberl, C++11 Implementation of Finite Elements In NGSolve. Preprint 30/2014, Institute for Analysis and Scientific Computing, TU Wien (2014). [Google Scholar]
- D.R. Smith, J.B. Pendry and M.C.K. Wiltshire, Metamaterials and negative refractive index. Science 305 (2004) 788–792. [Google Scholar]
- C.K.W. Tam, L. Auriault and F. Cambuli, Perfectly matched layer as an absorbing boundary condition for the linearized euler equations in open and ducted domains. J. Comput. Phys. 144 (1998) 213–234. [CrossRef] [MathSciNet] [Google Scholar]
- F.L. Teixeira and W.C. Chew, On causality and dynamic stability of perfectly matched layers for FDTD simulations. Micro. Opt. Tech. Lett. 17 (1998) 231–236. [CrossRef] [Google Scholar]
- E. Turkel and A. Yefet, Absorbing PML boundary layers for wave-like equations. Appl. Numer. Math. 27 (1998) 533–557. [CrossRef] [MathSciNet] [Google Scholar]
- V. Vinoles, Problèmes d’interface en présence de métamatériaux: modélisation, analyse et simulations, Ph.D. thesis, Université Paris-Saclay (ComUE) (2016). [Google Scholar]
- G. Wanner, E. Hairer and S.P. Norsett, Order stars and stability theorems. BIT 18 (1978) 475–489. [CrossRef] [MathSciNet] [Google Scholar]
- L. Zhao and A.C. Cangellaris, GT PML: generalize theory of perfectly matched layers and its application to the reflectionless truncation of finite-difference time-domain grids. IEEE Trans. Microwave Theory Tech. 44 (1996) 2555–2563. [CrossRef] [Google Scholar]
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.