{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,16]],"date-time":"2024-09-16T14:26:37Z","timestamp":1726496797845},"reference-count":33,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2015,11,1]],"date-time":"2015-11-01T00:00:00Z","timestamp":1446336000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Mathematics and Computers in Simulation"],"published-print":{"date-parts":[[2015,11]]},"DOI":"10.1016\/j.matcom.2015.01.009","type":"journal-article","created":{"date-parts":[[2015,6,19]],"date-time":"2015-06-19T16:39:15Z","timestamp":1434731955000},"page":"54-67","update-policy":"http:\/\/dx.doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":10,"special_numbering":"C","title":["A multigrid-based preconditioned solver for the Helmholtz equation with a discretization by 25-point difference scheme"],"prefix":"10.1016","volume":"117","author":[{"given":"Dongsheng","family":"Cheng","sequence":"first","affiliation":[]},{"given":"Zhiyong","family":"Liu","sequence":"additional","affiliation":[]},{"given":"Tingting","family":"Wu","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"key":"10.1016\/j.matcom.2015.01.009_br000005","first-page":"451","article-title":"Is the pollution effect of the FEM avoidable for the Helmholtz equation considering high wave numbers?","volume":"42","author":"Babu\u0161ka","year":"2000","journal-title":"SIAM Rev."},{"key":"10.1016\/j.matcom.2015.01.009_br000010","doi-asserted-by":"crossref","first-page":"631","DOI":"10.1016\/0021-9991(83)90139-0","article-title":"An iterative method for Helmholtz equation","volume":"49","author":"Bayliss","year":"1983","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.matcom.2015.01.009_br000015","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1006\/jcph.1994.1159","article-title":"A perfectly matched layer for the absorption of electromagnetic waves","volume":"114","author":"B\u00e9renger","year":"1994","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.matcom.2015.01.009_br000020","doi-asserted-by":"crossref","first-page":"522","DOI":"10.1016\/j.jmaa.2011.05.054","article-title":"A multigrid-based preconditioned Krylov subspace method for the Helmholtz equation with PML","volume":"383","author":"Chen","year":"2011","journal-title":"J. Math. Anal. Appl."},{"key":"10.1016\/j.matcom.2015.01.009_br000025","doi-asserted-by":"crossref","first-page":"799","DOI":"10.1137\/S0036142902400901","article-title":"An adaptive finite element method with perfectly matched absorbing layers for the wave scattering by periodic structures","volume":"41","author":"Chen","year":"2003","journal-title":"SIAM J. Numer. Anal."},{"key":"10.1016\/j.matcom.2015.01.009_br000030","doi-asserted-by":"crossref","first-page":"1240","DOI":"10.1016\/j.cam.2011.08.007","article-title":"An optimal 25-point finite difference scheme for the Helmholtz equation with PML","volume":"236","author":"Chen","year":"2011","journal-title":"J. Comput. Appl. Math."},{"key":"10.1016\/j.matcom.2015.01.009_br000035","doi-asserted-by":"crossref","first-page":"471","DOI":"10.1002\/(SICI)1097-0207(19991010)46:4<471::AID-NME684>3.0.CO;2-6","article-title":"Dispersion and pollution of the FEM sollution for the Helmholtz equation in one, two and three dimensions","volume":"46","author":"Deraemaeker","year":"1999","journal-title":"Int. J. Numer. Methods Eng."},{"key":"10.1016\/j.matcom.2015.01.009_br000040","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0377-0427(90)90252-U","article-title":"Matrix-dependent prolongations and restrictions in a blackbox multigrid solver","volume":"33","author":"de Zeeuw","year":"1990","journal-title":"J. Comput. Appl. Math."},{"key":"10.1016\/j.matcom.2015.01.009_br000045","doi-asserted-by":"crossref","first-page":"1167","DOI":"10.1080\/00207160701356076","article-title":"Multigrid based preconditioners for the numerical solution of two-dimensional heterogeneous problems in geophysics","volume":"84","author":"Duff","year":"2007","journal-title":"Int. J. Comput. Math."},{"key":"10.1016\/j.matcom.2015.01.009_br000050","doi-asserted-by":"crossref","first-page":"314","DOI":"10.1002\/cpa.3160320303","article-title":"Radiation boundary conditions for acoustic and elastic wave calculations","volume":"32","author":"Engquist","year":"1979","journal-title":"Comm. Pure Appl. Math."},{"key":"10.1016\/j.matcom.2015.01.009_br000055","doi-asserted-by":"crossref","first-page":"1471","DOI":"10.1137\/040615195","article-title":"A novel multigrid based preconditioner for heterogeneous Helmholtz problems","volume":"27","author":"Erlangga","year":"2006","journal-title":"SIAM J. Sci. Comput."},{"key":"10.1016\/j.matcom.2015.01.009_br000060","doi-asserted-by":"crossref","first-page":"629","DOI":"10.1016\/j.apnum.2004.01.009","article-title":"On a class of preconditioners for the Helmholtz equation","volume":"50","author":"Erlangga","year":"2004","journal-title":"Appl. Numer. Math."},{"key":"10.1016\/j.matcom.2015.01.009_br000065","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1090\/S0025-5718-99-01028-5","article-title":"Absorbing boundary conditions for electromagnetic wave propagation","volume":"68","author":"Feng","year":"1999","journal-title":"Math. Comp."},{"key":"10.1016\/j.matcom.2015.01.009_br000070","doi-asserted-by":"crossref","first-page":"2872","DOI":"10.1137\/080737538","article-title":"Discontinuous galerkin methods for the Helmholtz equation with large wave number","volume":"47","author":"Feng","year":"2009","journal-title":"SIAM J. Numer. Anal."},{"key":"10.1016\/j.matcom.2015.01.009_br000075","first-page":"425","article-title":"Conjuate gradient compiled with multigrid for an indefinite problems","volume":"vol. V","author":"Gozani","year":"1984"},{"key":"10.1016\/j.matcom.2015.01.009_br000080","doi-asserted-by":"crossref","first-page":"3061","DOI":"10.1121\/1.417118","article-title":"Application of the perfectly matched layer (PML) absorbing boundary condition to elastic wave propagation","volume":"100","author":"Hastings","year":"1996","journal-title":"J. Acoust. Soc. Am."},{"key":"10.1016\/j.matcom.2015.01.009_br000085","doi-asserted-by":"crossref","first-page":"1157","DOI":"10.1016\/j.apnum.2010.07.004","article-title":"Application of the shifted-Laplace preconditioner for iterative solution of a higher order finite element discretisation of the vector wave equation: First experiences","volume":"60","author":"Hooghiemstra","year":"2010","journal-title":"Appl. Numer. Math."},{"key":"10.1016\/j.matcom.2015.01.009_br000090","doi-asserted-by":"crossref","first-page":"1269","DOI":"10.1111\/j.1365-246X.2004.02289.x","article-title":"Mixed-grid and staggered-grid finite difference methods for frequency-domain acoustic wave modelling","volume":"157","author":"Hustedt","year":"2004","journal-title":"Geophys. J. Int."},{"key":"10.1016\/j.matcom.2015.01.009_br000095","doi-asserted-by":"crossref","first-page":"4207","DOI":"10.1002\/nme.1620382203","article-title":"Dispersion analysis and error estimation of galerkin finite element methods for the Helmholtz equation","volume":"38","author":"Ihlenburg","year":"1995","journal-title":"Int. J. Numer. Methods Eng."},{"key":"10.1016\/j.matcom.2015.01.009_br000100","doi-asserted-by":"crossref","first-page":"529","DOI":"10.1190\/1.1443979","article-title":"An optimal 9-point, finite-difference, frequency-space, 2-D scalar wave extrapolator","volume":"61","author":"Jo","year":"1996","journal-title":"Geophysics"},{"key":"10.1016\/j.matcom.2015.01.009_br000105","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1016\/j.cam.2011.07.021","article-title":"GPU implementation of a Helmholtz Krylov solver preconditioned by a shifted Laplace multigrid method","volume":"236","author":"Knibbe","year":"2011","journal-title":"J. Comput. Appl. Math."},{"year":"2002","series-title":"Preconditioned Iterative Solution of the 2D Helmholtz equation, Report 02\/12","author":"Laird","key":"10.1016\/j.matcom.2015.01.009_br000110"},{"key":"10.1016\/j.matcom.2015.01.009_br000115","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1190\/1.2759835","article-title":"3D finite-difference frequency-domain modeling of visco-acoustic wave propagation using a massively parallel direct solver: A feasibility study","volume":"72","author":"Operto","year":"2007","journal-title":"Geophysics"},{"key":"10.1016\/j.matcom.2015.01.009_br000120","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1016\/j.jcp.2007.03.033","article-title":"A parallel multigrid-based preconditioner for the 3D heterogeneous high-frequency Helmholtz equation","volume":"224","author":"Riyanti","year":"2007","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.matcom.2015.01.009_br000125","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1137\/0907058","article-title":"GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear system","volume":"7","author":"Saad","year":"1986","journal-title":"SIAM J. Sci. Stat. Comput."},{"key":"10.1016\/j.matcom.2015.01.009_br000130","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1190\/1.1444323","article-title":"A frequency-space 2-D scalar wave extrapolator using extended 25-point finite-difference operator","volume":"63","author":"Shin","year":"1998","journal-title":"Geophysics"},{"key":"10.1016\/j.matcom.2015.01.009_br000135","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1016\/S0045-7825(98)00023-1","article-title":"High-order finite difference methods for the Helmholtz equation","volume":"163","author":"Singer","year":"1998","journal-title":"Comput. Methods Appl. Mech. Engrg."},{"key":"10.1016\/j.matcom.2015.01.009_br000140","doi-asserted-by":"crossref","first-page":"439","DOI":"10.1016\/j.jcp.2004.06.010","article-title":"A perfectly matched layer for the Helmholtz equation in a semi-infinite strip","volume":"201","author":"Singer","year":"2004","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.matcom.2015.01.009_br000145","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1016\/j.cam.2006.03.008","article-title":"Compact finite difference schemes of sixth order for the Helmholtz equation","volume":"203","author":"Sutmann","year":"2007","journal-title":"J. Comput. Appl. Math."},{"key":"10.1016\/j.matcom.2015.01.009_br000150","doi-asserted-by":"crossref","first-page":"1779","DOI":"10.1190\/1.1444472","article-title":"Accurate viscoelastic modeling by frequency-domain finite differences using rotated operators","volume":"63","author":"\u0160tekl","year":"1998","journal-title":"Geophysics"},{"key":"10.1016\/j.matcom.2015.01.009_br000155","doi-asserted-by":"crossref","first-page":"603","DOI":"10.1002\/nla.634","article-title":"A multigrid-based shifted Laplacian preconditioner for a fourth-order Helmholtz discretization","volume":"16","author":"Umetani","year":"2009","journal-title":"Numer. Linear Algebra Appl."},{"key":"10.1016\/j.matcom.2015.01.009_br000160","doi-asserted-by":"crossref","first-page":"631","DOI":"10.1137\/0913035","article-title":"Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems","volume":"13","author":"Van Der Vorst","year":"1992","journal-title":"SIAM J. Sci. Stat. Comput."},{"key":"10.1016\/j.matcom.2015.01.009_br000165","doi-asserted-by":"crossref","first-page":"1942","DOI":"10.1137\/060661491","article-title":"Spectral analysis of the discrete Helmholtz operator with a shifted Laplacian","volume":"29","author":"Van Gijzen","year":"2007","journal-title":"SIAM J. Sci. Comput."}],"container-title":["Mathematics and Computers in Simulation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0378475415001160?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0378475415001160?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2018,9,21]],"date-time":"2018-09-21T16:54:11Z","timestamp":1537548851000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0378475415001160"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,11]]},"references-count":33,"alternative-id":["S0378475415001160"],"URL":"https:\/\/doi.org\/10.1016\/j.matcom.2015.01.009","relation":{},"ISSN":["0378-4754"],"issn-type":[{"type":"print","value":"0378-4754"}],"subject":[],"published":{"date-parts":[[2015,11]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"A multigrid-based preconditioned solver for the Helmholtz equation with a discretization by 25-point difference scheme","name":"articletitle","label":"Article Title"},{"value":"Mathematics and Computers in Simulation","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.matcom.2015.01.009","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"Copyright \u00a9 2015 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier Ltd. All rights reserved.","name":"copyright","label":"Copyright"}]}}