Perfectly matched layer truncation for parabolic wave equation models

Abstract

Restricted accessMoreSectionsView PDF ToolsAdd to favoritesDownload CitationsTrack Citations ShareShare onFacebookTwitterLinked InRedditEmail Cite this article Levy Mireille F. 2001Perfectly matched layer truncation for parabolic wave equation modelsProc. R. Soc. Lond. A.4572609–2624http://doi.org/10.1098/rspa.2001.0848SectionRestricted accessResearch articlePerfectly matched layer truncation for parabolic wave equation models Mireille F. Levy Mireille F. Levy Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire OX11 0QX, UK Google Scholar Find this author on PubMed Search for more papers by this author Mireille F. Levy Mireille F. Levy Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire OX11 0QX, UK Google Scholar Find this author on PubMed Search for more papers by this author Published:08 November 2001https://doi.org/10.1098/rspa.2001.0848AbstractSolutions of the parabolic wave equation are extended to complex values of the height variable. The fast decay of the solutions in certain directions of the complex plane is used to improve parabolic wave equation solvers: the solution is marched on a suitably chosen contour in the complex plane rather than on the real line. This interpretation of Bérenger's perfectly matched layer allows extremely efficient truncation of the computational domain with a split–step/Fourier algorithm. The theory is developed for both the wide–angle and narrow–angle parabolic wave equations, and numerical results are presented. Previous ArticleNext Article VIEW FULL TEXT DOWNLOAD PDF FiguresRelatedReferencesDetailsCited by Petrov P, Ehrhardt M, Tyshchenko A and Petrov P (2020) Wide-angle mode parabolic equations for the modelling of horizontal refraction in underwater acoustics and their numerical solution on unbounded domains, Journal of Sound and Vibration, 10.1016/j.jsv.2020.115526, 484, (115526), Online publication date: 1-Oct-2020. Ramamurti A and Calvo D (2019) Multisector parabolic-equation approach to compute acoustic scattering by noncanonically shaped impenetrable objects, Physical Review E, 10.1103/PhysRevE.100.063309, 100:6 Scrinzi A, Stimming H and Mauser N (2014) On the non-equivalence of perfectly matched layers and exterior complex scaling, Journal of Computational Physics, 10.1016/j.jcp.2014.03.007, 269, (98-107), Online publication date: 1-Jul-2014. Chen H, Zhou H, Lin H and Wang S (2013) Application of perfectly matched layer for scalar arbitrarily wide-angle wave equations, GEOPHYSICS, 10.1190/geo2012-0062.1, 78:1, (T29-T39), Online publication date: 1-Jan-2013. Sheng Q and Sun H (2015) Asymptotic Stability of an Eikonal Transformation Based ADI Method for the Paraxial Helmholtz Equation at High Wave Numbers, Communications in Computational Physics, 10.4208/cicp.100811.090112a, 12:4, (1275-1292), Online publication date: 1-Oct-2012. Chen H, Zhou H, Lin H and Wang S (2012) Application of perfectly matched layer for scalar arbitrarily wide-angle wave equations SEG Technical Program Expanded Abstracts 2012, 10.1190/segam2012-0452.1, , (1-5), Online publication date: 1-Sep-2012. Ozbayat S and Janaswamy R Effective Local Absorbing Boundary Conditions for a Finite Difference Implementation of the Parabolic Equation, IEEE Transactions on Antennas and Propagation, 10.1109/TAP.2011.2122300, 59:5, (1616-1625) Heidari A and Guddati M (2006) Highly accurate absorbing boundary conditions for wide-angle wave equations, GEOPHYSICS, 10.1190/1.2192914, 71:3, (S85-S97), Online publication date: 1-May-2006. von Winckel G, Krishna S and Coutsias E (2006) Spectral element modeling of semiconductor heterostructures, Mathematical and Computer Modelling, 10.1016/j.mcm.2005.05.028, 43:5-6, (582-591), Online publication date: 1-Mar-2006. Hagstrom T (2003) New Results on Absorbing Layers and Radiation Boundary Conditions Topics in Computational Wave Propagation, 10.1007/978-3-642-55483-4_1, (1-42), . Pled F and Desceliers C (2021) Review and Recent Developments on the Perfectly Matched Layer (PML) Method for the Numerical Modeling and Simulation of Elastic Wave Propagation in Unbounded Domains, Archives of Computational Methods in Engineering, 10.1007/s11831-021-09581-y This Issue08 November 2001Volume 457Issue 2015 Article InformationDOI:https://doi.org/10.1098/rspa.2001.0848Published by:Royal SocietyPrint ISSN:1364-5021Online ISSN:1471-2946History: Published online08/11/2001Published in print08/11/2001 License: Citations and impact Keywordswave equationparabolic equation modelselectromagnetic scatteringperfectly matched layer