{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,3]],"date-time":"2025-12-03T17:44:55Z","timestamp":1764783895752,"version":"3.37.3"},"reference-count":25,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2016,8,26]],"date-time":"2016-08-26T00:00:00Z","timestamp":1472169600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2016,8,26]],"date-time":"2016-08-26T00:00:00Z","timestamp":1472169600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/100000181","name":"Air Force Office of Scientific Research","doi-asserted-by":"publisher","award":["FA9550-11-1-0281","FA9550-12-1-0343"],"award-info":[{"award-number":["FA9550-11-1-0281","FA9550-12-1-0343"]}],"id":[{"id":"10.13039\/100000181","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000181","name":"Air Force Office of Scientific Research","doi-asserted-by":"publisher","award":["FA9550-12-1-0455"],"award-info":[{"award-number":["FA9550-12-1-0455"]}],"id":[{"id":"10.13039\/100000181","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-1115709"],"award-info":[{"award-number":["DMS-1115709"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100007709","name":"Michigan State University","doi-asserted-by":"publisher","award":["SPG-RG100059"],"award-info":[{"award-number":["SPG-RG100059"]}],"id":[{"id":"10.13039\/100007709","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2017,2]]},"DOI":"10.1007\/s10915-016-0268-8","type":"journal-article","created":{"date-parts":[[2016,8,26]],"date-time":"2016-08-26T14:55:22Z","timestamp":1472223322000},"page":"896-921","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Method of Lines Transpose: An Efficient Unconditionally Stable Solver for Wave Propagation"],"prefix":"10.1007","volume":"70","author":[{"given":"Matthew","family":"Causley","sequence":"first","affiliation":[]},{"given":"Andrew","family":"Christlieb","sequence":"additional","affiliation":[]},{"given":"Eric","family":"Wolf","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2016,8,26]]},"reference":[{"issue":"2","key":"268_CR1","doi-asserted-by":"publisher","first-page":"536","DOI":"10.1006\/jcph.2000.6547","volume":"162","author":"B Alpert","year":"2000","unstructured":"Alpert, B., Greengard, L., Hagstrom, T.: An integral evolution formula for the wave equation. J. Comput. Phys. 162(2), 536\u2013543 (2000)","journal-title":"J. Comput. Phys."},{"issue":"1","key":"268_CR2","doi-asserted-by":"publisher","first-page":"270","DOI":"10.1006\/jcph.2002.7093","volume":"180","author":"B Alpert","year":"2002","unstructured":"Alpert, B., Greengard, L., Hagstrom, T.: Nonreflecting boundary conditions for the time-dependent wave equation. J. Comput. Phys. 180(1), 270\u2013296 (2002)","journal-title":"J. Comput. Phys."},{"key":"268_CR3","doi-asserted-by":"publisher","first-page":"446","DOI":"10.1038\/324446a0","volume":"324","author":"J Barnes","year":"1986","unstructured":"Barnes, J., Hut, P.: A hierarchical O(N log N) force-calculation algorithm. Nature 324, 446\u2013449 (1986)","journal-title":"Nature"},{"key":"268_CR4","volume-title":"Plasma Physics via Computer Simulation, Course Notes for Electrical Engineering and Computer Sciences","author":"CK Birdsall","year":"1976","unstructured":"Birdsall, C.K., Langdon, A.B.: Plasma Physics via Computer Simulation, Course Notes for Electrical Engineering and Computer Sciences. McGraw-Hill, New York (1976)"},{"issue":"1","key":"268_CR5","doi-asserted-by":"publisher","first-page":"107","DOI":"10.1090\/S0002-9947-1906-1500736-1","volume":"7","author":"GD Birkhoff","year":"1906","unstructured":"Birkhoff, G.D.: General mean value and remainder theorems with applications to mechanical differentiation and quadrature. Trans. Am. Math. Soc. 7(1), 107\u2013136 (1906). (English)","journal-title":"Trans. Am. Math. Soc."},{"issue":"6","key":"268_CR6","doi-asserted-by":"publisher","first-page":"2009","DOI":"10.1016\/j.jcp.2009.11.020","volume":"229","author":"OP Bruno","year":"2010","unstructured":"Bruno, O.P., Lyon, M.: High-order unconditionally stable FC-AD solvers for general smooth domains I. Basic elements. J. Comput. Phys. 229(6), 2009\u20132033 (2010)","journal-title":"J. Comput. Phys."},{"issue":"1","key":"268_CR7","doi-asserted-by":"publisher","first-page":"220","DOI":"10.1137\/130932685","volume":"52","author":"M Causley","year":"2014","unstructured":"Causley, M., Christlieb, A.: High order a-stable schemes for the wave equation using successive convolution. SIAM J. Numer. Anal. 52(1), 220\u2013235 (2014)","journal-title":"SIAM J. Numer. Anal."},{"issue":"290","key":"268_CR8","doi-asserted-by":"publisher","first-page":"2763","DOI":"10.1090\/S0025-5718-2014-02834-2","volume":"83","author":"M Causley","year":"2014","unstructured":"Causley, M., Christlieb, A., Ong, B., Van Groningen, L.: Method of lines transpose: an implicit solution to the wave equation. Math. Comput. 83(290), 2763\u20132786 (2014)","journal-title":"Math. Comput."},{"key":"268_CR9","doi-asserted-by":"crossref","unstructured":"M.\u00a0F. Causley, H.\u00a0Cho, A.\u00a0J. Christlieb, and D.\u00a0C. Seal, Method of lines transpose: High order L-stable O(N) schemes for parabolic equations using successive convolution, ArXiv e-prints (2015)","DOI":"10.1137\/15M1035094"},{"issue":"2","key":"268_CR10","doi-asserted-by":"publisher","first-page":"468","DOI":"10.1006\/jcph.1999.6355","volume":"155","author":"H Cheng","year":"1999","unstructured":"Cheng, H., Greengard, L., Rokhlin, V.: A fast adaptive multipole algorithm in three dimensions. J. Comput. Phys. 155(2), 468\u2013498 (1999)","journal-title":"J. Comput. Phys."},{"issue":"2","key":"268_CR11","doi-asserted-by":"publisher","first-page":"616","DOI":"10.1016\/j.jcp.2005.06.006","volume":"211","author":"H Cheng","year":"2006","unstructured":"Cheng, H., Huang, J., Leiterman, T.J.: An adaptive fast solver for the modified Helmholtz equation in two dimensions. J. Comput. Phys. 211(2), 616\u2013637 (2006)","journal-title":"J. Comput. Phys."},{"issue":"1\u20133","key":"268_CR12","doi-asserted-by":"publisher","first-page":"306","DOI":"10.1016\/j.cpc.2004.06.076","volume":"164","author":"AJ Christlieb","year":"2004","unstructured":"Christlieb, A.J., Krasny, R., Verboncoeur, J.P.: A treecode algorithm for simulating electron dynamics in a Penning-Malmberg trap. Comput. Phys. Commun. 164(1\u20133), 306\u2013310 (2004)","journal-title":"Comput. Phys. Commun."},{"issue":"3","key":"268_CR13","doi-asserted-by":"publisher","first-page":"7","DOI":"10.1109\/74.250128","volume":"35","author":"R Coifman","year":"1993","unstructured":"Coifman, R., Rokhlin, V., Wandzura, S.: The fast multipole method for the wave equation: a pedestrian prescription. IEEE Trans. Antennas Propaga. 35(3), 7\u201312 (1993)","journal-title":"IEEE Trans. Antennas Propaga."},{"key":"268_CR14","unstructured":"Fornberg, B.: A short proof of the unconditional stability of the ADI-FDTD scheme, 9810751, pp. 5\u20138"},{"key":"268_CR15","unstructured":"Fornberg, B., Zuev, J., Lee, J.: Stability and accuracy of time-extrapolated ADI-FDTD methods for solving wave equations, 9810751, no. (November 2005)"},{"issue":"3","key":"268_CR16","doi-asserted-by":"publisher","first-page":"796","DOI":"10.1137\/S1064827500381148","volume":"24","author":"Z Gimbutas","year":"2002","unstructured":"Gimbutas, Z., Rokhlin, V.: A generalized fast multipole method for nonoscillatory kernels. SIAM J. Sci. Comput. 24(3), 796\u2013817 (2002)","journal-title":"SIAM J. Sci. Comput."},{"issue":"2","key":"268_CR17","doi-asserted-by":"publisher","first-page":"325","DOI":"10.1016\/0021-9991(87)90140-9","volume":"73","author":"L Greengard","year":"1987","unstructured":"Greengard, L., Rokhlin, V.: A fast algorithm for particle simulations. J. Comput. Phys. 73(2), 325\u2013348 (1987)","journal-title":"J. Comput. Phys."},{"issue":"3","key":"268_CR18","doi-asserted-by":"publisher","first-page":"1292","DOI":"10.1137\/S003614290342827X","volume":"42","author":"HO Kreiss","year":"2004","unstructured":"Kreiss, H.O., Petersson, N.A., Ystr\u00f6m, J.: Difference approximations of the neumann problem for the second order wave equation. SIAM J. Numer. Anal. 42(3), 1292\u20131323 (2004)","journal-title":"SIAM J. Numer. Anal."},{"issue":"2\u20133","key":"268_CR19","doi-asserted-by":"publisher","first-page":"455","DOI":"10.1016\/j.laa.2003.10.020","volume":"415","author":"JR Li","year":"2006","unstructured":"Li, J.R.: Low order approximation of the spherical nonreflecting boundary kernel for the wave equation. Linear Algebra Appl. 415(2\u20133), 455\u2013468 (2006)","journal-title":"Linear Algebra Appl."},{"issue":"10","key":"268_CR20","doi-asserted-by":"publisher","first-page":"3858","DOI":"10.1016\/j.jcp.2009.02.022","volume":"228","author":"P Li","year":"2009","unstructured":"Li, P., Johnston, H., Krasny, R.: A Cartesian treecode for screened coulomb interactions. J. Comput. Phys. 228(10), 3858\u20133868 (2009)","journal-title":"J. Comput. Phys."},{"issue":"2","key":"268_CR21","doi-asserted-by":"publisher","first-page":"879","DOI":"10.1006\/jcph.2001.6862","volume":"172","author":"K Lindsay","year":"2001","unstructured":"Lindsay, K., Krasny, R.: A particle method and adaptive treecode for vortex sheet motion in three-dimensional flow. J. Comput. Phys. 172(2), 879\u2013907 (2001)","journal-title":"J. Comput. Phys."},{"issue":"9","key":"268_CR22","doi-asserted-by":"publisher","first-page":"3358","DOI":"10.1016\/j.jcp.2010.01.006","volume":"229","author":"M Lyon","year":"2010","unstructured":"Lyon, M., Bruno, O.P.: High-order unconditionally stable FC-AD solvers for general smooth domains II. Elliptic, parabolic and hyperbolic PDEs; theoretical considerations. J. Comput. Phys. 229(9), 3358\u20133381 (2010)","journal-title":"J. Comput. Phys."},{"issue":"10","key":"268_CR23","doi-asserted-by":"publisher","first-page":"1743","DOI":"10.1109\/22.873904","volume":"48","author":"T Namiki","year":"2000","unstructured":"Namiki, T.: 3-d adi-fdtd method-unconditionally stable time-domain algorithm for solving full vector maxwell\u2019s equations. Microw. Theory Tech. IEEE Trans. 48(10), 1743\u20131748 (2000)","journal-title":"Microw. Theory Tech. IEEE Trans."},{"issue":"19","key":"268_CR24","doi-asserted-by":"publisher","first-page":"7289","DOI":"10.1016\/j.jcp.2009.06.025","volume":"228","author":"DN Smithe","year":"2009","unstructured":"Smithe, D.N., Cary, J.R., Carlsson, J.A.: Divergence preservation in the adi algorithms for electromagnetics. J. Comput. Phys. 228(19), 7289\u20137299 (2009)","journal-title":"J. Comput. Phys."},{"key":"268_CR25","doi-asserted-by":"publisher","unstructured":"Wolf, E.M., Causley, M.F., Christlieb, A.J., Bettencourt, M.: A particle-in-cell method for the simulation of plasmas based on an unconditionally stable field solver. J. Comput. Phys. (2016). doi:\n                    10.1016\/j.jcp.2016.08.006","DOI":"10.1016\/j.jcp.2016.08.006"}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-016-0268-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10915-016-0268-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-016-0268-8","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-016-0268-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,17]],"date-time":"2020-05-17T09:13:28Z","timestamp":1589706808000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10915-016-0268-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,8,26]]},"references-count":25,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2017,2]]}},"alternative-id":["268"],"URL":"https:\/\/doi.org\/10.1007\/s10915-016-0268-8","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"type":"print","value":"0885-7474"},{"type":"electronic","value":"1573-7691"}],"subject":[],"published":{"date-parts":[[2016,8,26]]},"assertion":[{"value":"15 December 2015","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 June 2016","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 August 2016","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 August 2016","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}