{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,1]],"date-time":"2026-09-01T08:10:26Z","timestamp":1788250226048,"version":"build-2803163510"},"reference-count":23,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2016,8,16]],"date-time":"2016-08-16T00:00:00Z","timestamp":1471305600000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Adv Comput Math"],"published-print":{"date-parts":[[2017,2]]},"DOI":"10.1007\/s10444-016-9475-y","type":"journal-article","created":{"date-parts":[[2016,8,16]],"date-time":"2016-08-16T01:10:00Z","timestamp":1471309800000},"page":"45-76","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":25,"title":["An improved sweeping domain decomposition preconditioner for the Helmholtz equation"],"prefix":"10.1007","volume":"43","author":[{"given":"Christiaan C.","family":"Stolk","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2016,8,16]]},"reference":[{"issue":"1","key":"9475_CR1","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1137\/S0895479899358194","volume":"23","author":"PR Amestoy","year":"2001","unstructured":"Amestoy, P.R., Duff, I.S., Koster, J., L\u2019Excellent, J.-Y.: A fully asynchronous multifrontal solver using distributed dynamic scheduling. SIAM J. Matrix Anal. Appl. 23(1), 15\u201341 (2001)","journal-title":"SIAM J. Matrix Anal. Appl."},{"issue":"3-4","key":"9475_CR2","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1016\/0045-7825(95)00890-X","volume":"128","author":"I Babu\u0161ka","year":"1995","unstructured":"Babu\u0161ka, I., Ihlenburg, F., Paik, E.T., Sauter, S.A.: A generalized finite element method for solving the Helmholtz equation in two dimensions with minimal pollution. Comput. Methods Appl. Mech Eng. 128(3-4), 325\u2013359 (1995)","journal-title":"Comput. Methods Appl. Mech Eng."},{"issue":"4","key":"9475_CR3","doi-asserted-by":"crossref","first-page":"663","DOI":"10.1002\/nla.1860","volume":"20","author":"H Calandra","year":"2013","unstructured":"Calandra, H., Gratton, S., Pinel, X., Vasseur, X.: An improved two-grid preconditioner for the solution of three-dimensional Helmholtz problems in heterogeneous media. Numer. Linear Algebra Appl. 20(4), 663\u2013688 (2013)","journal-title":"Numer. Linear Algebra Appl."},{"issue":"4","key":"9475_CR4","doi-asserted-by":"crossref","first-page":"2331","DOI":"10.1137\/130917144","volume":"51","author":"Z Chen","year":"2013","unstructured":"Chen, Z., Xiang, X.: A source transfer domain decomposition method for Helmholtz equations in unbounded domain. SIAM J. Numer. Anal. 51(4), 2331\u20132356 (2013)","journal-title":"SIAM J. Numer. Anal."},{"issue":"2","key":"9475_CR5","doi-asserted-by":"crossref","first-page":"686","DOI":"10.1137\/100804644","volume":"9","author":"B Engquist","year":"2011","unstructured":"Engquist, B., Ying, L.: Sweeping preconditioner for the Helmholtz equation: moving perfectly matched layers. Multiscale Model Simul. 9(2), 686\u2013710 (2011)","journal-title":"Multiscale Model Simul."},{"issue":"1","key":"9475_CR6","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1007\/s11831-007-9013-7","volume":"15","author":"YA Erlangga","year":"2008","unstructured":"Erlangga, Y. A.: Advances in iterative methods and preconditioners for the Helmholtz equation. Arch. Comput. Methods Eng. 15(1), 37\u201366 (2008)","journal-title":"Arch. Comput. Methods Eng."},{"key":"9475_CR7","doi-asserted-by":"crossref","unstructured":"Ernst, O.G., Gander, M.J.: Why it is difficult to solve Helmholtz problems with classical iterative methods. In: Graham, I., Hou, T., Lakkis, O., Scheichl, R. (eds.) Numerical Analysis of Multiscale Problems. Springer (2011)","DOI":"10.1007\/978-3-642-22061-6_10"},{"issue":"2","key":"9475_CR8","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1002\/fld.1433","volume":"55","author":"MJ Gander","year":"2007","unstructured":"Gander, M.J., Halpern, L., Magoul\u00e8s, F.: An optimized Schwarz method with two-sided Robin transmission conditions for the Helmholtz equation. Internat. J. Numer. Methods Fluids 55(2), 163\u2013175 (2007)","journal-title":"Internat. J. Numer. Methods Fluids"},{"key":"9475_CR9","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1137\/0710032","volume":"10","author":"A George","year":"1973","unstructured":"George, A.: Nested dissection of a regular finite element mesh. SIAM J. Numer. Anal. 10, 345\u2013363 (1973)","journal-title":"SIAM J. Numer. Anal."},{"issue":"2","key":"9475_CR10","doi-asserted-by":"crossref","first-page":"529","DOI":"10.1190\/1.1443979","volume":"61","author":"C-H Jo","year":"1996","unstructured":"Jo, C.-H., Shin, C., Suh, J.H.: An optimal 9-point, finite-difference, frequency-space, 2-D scalar wave extrapolator. Geophysics 61(2), 529\u2013537 (1996)","journal-title":"Geophysics"},{"key":"9475_CR11","unstructured":"Johnson, S.G.: Notes on perfectly matched layers. http:\/\/math.mit.edu\/stevenj\/18.369\/pml.pdf (2010)"},{"issue":"3","key":"9475_CR12","doi-asserted-by":"crossref","first-page":"C194","DOI":"10.1137\/120871985","volume":"35","author":"J Poulson","year":"2013","unstructured":"Poulson, J., Engquist, B., Li, S., Ying, L.: A parallel sweeping preconditioner for heterogeneous 3D Helmholtz equations. SIAM J. Sci Comput. 35 (3), C194\u2013C212 (2013)","journal-title":"SIAM J. Sci Comput."},{"issue":"1","key":"9475_CR13","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1016\/j.jcp.2007.03.033","volume":"224","author":"C Riyanti","year":"2007","unstructured":"Riyanti, C., Kononov, A., Erlangga, Y., Vuik, C., Oosterlee, C., Plessix, R.-E., Mulder, W.: A parallel multigrid-based preconditioner for the 3D heterogeneous high-frequency Helmholtz equation. J. Comput. Phys. 224(1), 431 \u2013 448 (2007). Special Issue Dedicated to Professor Piet Wesseling on the occasion of his retirement from Delft University of Technology","journal-title":"J. Comput. Phys."},{"issue":"1","key":"9475_CR14","doi-asserted-by":"crossref","first-page":"477","DOI":"10.1016\/j.jcp.2007.04.017","volume":"226","author":"A Sch\u00e4dle","year":"2007","unstructured":"Sch\u00e4dle, A., Zschiedrich, L., Burger, S., Klose, R., Schmidt, F.: Domain decomposition method for Maxwell\u2019s equations: scattering off periodic structures. J. Comput. Phys. 226(1), 477\u2013493 (2007)","journal-title":"J. Comput. Phys."},{"key":"9475_CR15","doi-asserted-by":"crossref","first-page":"240","DOI":"10.1016\/j.jcp.2013.01.039","volume":"241","author":"CC Stolk","year":"2013","unstructured":"Stolk, C.C.: A rapidly converging domain decomposition method for the Helmholtz equation. J. Comput. Phys. 241, 240\u2013252 (2013)","journal-title":"J. Comput. Phys."},{"key":"9475_CR16","doi-asserted-by":"crossref","first-page":"618","DOI":"10.1016\/j.jcp.2016.03.023","volume":"314","author":"CC Stolk","year":"2016","unstructured":"Stolk, C.C.: A dispersion minimizing scheme for the 3-D Helmholtz equation based on ray theory. J. Comput. Phys. 314, 618\u2013646 (2016)","journal-title":"J. Comput. Phys."},{"issue":"6","key":"9475_CR17","doi-asserted-by":"crossref","first-page":"A2819","DOI":"10.1137\/13092349X","volume":"36","author":"CC Stolk","year":"2014","unstructured":"Stolk, C.C., Ahmed, M., Bhowmik, S.K.: A multigrid method for the Helmholtz equation with optimized coarse grid corrections. SIAM J. Sci. Comput. 36(6), A2819\u2013A2841 (2014)","journal-title":"SIAM J. Sci. Comput."},{"key":"9475_CR18","volume-title":"Multigrid","author":"U Trottenberg","year":"2001","unstructured":"Trottenberg, U., Oosterlee, C.W., Sch\u00fcller, A.: Multigrid. Academic Press Inc., San Diego, CA (2001). With contributions by A. Brandt, P. Oswald and K. St\u00fcben"},{"issue":"1","key":"9475_CR19","doi-asserted-by":"crossref","first-page":"272","DOI":"10.1016\/j.jcp.2012.08.016","volume":"232","author":"E Turkel","year":"2013","unstructured":"Turkel, E., Gordon, D., Gordon, R., Tsynkov, S.: Compact 2D and 3D sixth order schemes for the Helmholtz equation with variable wave number. J. Comput. Phys. 232(1), 272\u2013287 (2013)","journal-title":"J. Comput. Phys."},{"key":"9475_CR20","unstructured":"Vion, A.: Multi-domain approaches for the solution of high-frequency time-harmonic propagation problems, PhD Thesis, Universit\u00e9 de Li\u00e8ge (2014)"},{"issue":"0","key":"9475_CR21","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1016\/j.jcp.2014.02.015","volume":"266","author":"A Vion","year":"2014","unstructured":"Vion, A., Geuzaine, C.: Double sweep preconditioner for optimized schwarz methods applied to the Helmholtz problem. J. Comput. Phys. 266(0), 171\u2013190 (2014)","journal-title":"J. Comput. Phys."},{"key":"9475_CR22","doi-asserted-by":"crossref","first-page":"857","DOI":"10.1111\/j.1365-2478.2011.00982.x","volume":"59","author":"S Wang","year":"2011","unstructured":"Wang, S., De Hoop, M.V., Xia, J.: On 3D modeling of seismic wave propagation via a structured parallel multifrontal direct Helmholtz solver. Geophys. Prospect. 59, 857\u2013873 (2011)","journal-title":"Geophys. Prospect."},{"key":"9475_CR23","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1016\/j.jcp.2015.11.040","volume":"308","author":"L Zepeda-N\u00fanez","year":"2016","unstructured":"Zepeda-N\u00fanez, L., Demanet, L.: The method of polarized traces for the 2D Helmholtz equation. J. Comput. Phys. 308, 347\u2013388 (2016)","journal-title":"J. Comput. Phys."}],"container-title":["Advances in Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-016-9475-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10444-016-9475-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-016-9475-y","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-016-9475-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,12]],"date-time":"2019-09-12T15:41:12Z","timestamp":1568302872000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10444-016-9475-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,8,16]]},"references-count":23,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2017,2]]}},"alternative-id":["9475"],"URL":"https:\/\/doi.org\/10.1007\/s10444-016-9475-y","relation":{},"ISSN":["1019-7168","1572-9044"],"issn-type":[{"value":"1019-7168","type":"print"},{"value":"1572-9044","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,8,16]]}}}