{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,25]],"date-time":"2026-08-25T10:56:55Z","timestamp":1787655415795,"version":"build-2736575974"},"reference-count":45,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2006,1]]},"abstract":"<jats:p>A scheme for the solution of the time\u2010dependent Maxwell\u2019s equations on composite overlapping grids is described. The method uses high\u2010order accurate approximations in space and time for Maxwell\u2019s equations written as a second\u2010order vector wave equation. High\u2010order accurate symmetric difference approximations to the generalized Laplace operator are constructed for curvilinear component grids. The modified equation approach is used to develop high\u2010order accurate approximations that use only three time levels and have the same time\u2010stepping restriction as the second\u2010order scheme. Discrete boundary conditions for perfect electrical conductors and for material interfaces are developed and analyzed. The implementation is optimized for component grids that are Cartesian, resulting in a fast and efficient method. The solver runs on parallel machines with each component grid distributed across one or more processors. Numerical results in two and three dimensions are presented for the fourth\u2010order accurate version of the method. These results demonstrate the accuracy and efficiency of the approach.<\/jats:p>","DOI":"10.1137\/050644379","type":"journal-article","created":{"date-parts":[[2006,10,23]],"date-time":"2006-10-23T11:30:50Z","timestamp":1161603050000},"page":"1730-1765","source":"Crossref","is-referenced-by-count":70,"title":["A High\u2010Order Accurate Parallel Solver for Maxwell\u2019s Equations on Overlapping Grids"],"prefix":"10.1137","volume":"28","author":[{"given":"William D.","family":"Henshaw","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,10,20]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1023\/A:1011520202197"},{"key":"R2","unstructured":"C. A. Balanis,\n                      Advanced Engineering Electromagnetics\n                      , John Wiley & Sons, New York, 1989."},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(90)90196-8"},{"key":"R4","doi-asserted-by":"crossref","unstructured":"G. C. Cohen,\n                      Higher\u2010Order Numerical Methods for Transient Wave Equations\n                      , Springer, New York, 2002.","DOI":"10.1007\/978-3-662-04823-8"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1007\/s002110100388"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1190\/1.1442040"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1109\/75.622536"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1137\/S0036139997323383"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.2001.6719"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1998.5883"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1137\/S106482759833320X"},{"key":"R12","doi-asserted-by":"crossref","unstructured":"B. Fornberg,\n                      A Practical Guide to Pseudospectral Methods\n                      , Cambridge University Press, Cambridge, UK, 1996.","DOI":"10.1017\/CBO9780511626357"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1109\/22.536021"},{"key":"R14","unstructured":"B. Gustafsson, H.\u2010O. Kreiss, and J. Oliger,\n                      Time Dependent Problems and Difference Methods\n                      , John Wiley & Sons, New York, 1995."},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1137\/030602459"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827503425900"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1016\/S1631-0721(02)01425-0"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142900375761"},{"key":"R19","unstructured":"W. Henshaw,\n                      Mappings for Overture, a Description of the Mapping Class and Documentation for Many Useful Mappings\n                      , Research report UCRL\u2010MA\u2010132239, Lawrence Livermore National Laboratory, Livermore, CA, 1998."},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1016\/0045-7930(94)90053-1"},{"key":"R21","doi-asserted-by":"publisher","DOI":"10.1137\/040603735"},{"key":"R22","doi-asserted-by":"publisher","DOI":"10.1016\/S0021-9991(03)00323-1"},{"key":"R23","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.2002.7118"},{"key":"R24","doi-asserted-by":"publisher","DOI":"10.1109\/TNS.1983.4333176"},{"key":"R25","unstructured":"J. Jin,\n                      The Finite Element Method in Electromagnetics\n                      , John Wiley & Sons, New York, 1993."},{"key":"R26","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827598334666"},{"key":"R27","doi-asserted-by":"publisher","DOI":"10.1137\/040604728"},{"key":"R28","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142901397435"},{"key":"R29","unstructured":"J. Lambert,\n                      Computational Methods in Ordinary Differential Equations\n                      , Cambridge University Press, New York, 1973."},{"key":"R30","doi-asserted-by":"publisher","DOI":"10.1109\/22.120108"},{"key":"R31","doi-asserted-by":"crossref","unstructured":"R. B. Lehoucq, D. C. Sorensen, and C. Yang,\n                      ARPACK Users\u2019 Guide: Solution of Large\u2010Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods\n                      , SIAM, Philadelphia, 1998.","DOI":"10.1137\/1.9780898719628"},{"key":"R32","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1995.1114"},{"key":"R33","doi-asserted-by":"publisher","DOI":"10.1007\/BF01396415"},{"key":"R34","unstructured":"D. Quinlan,\n                      A++\/P++ Class Libraries\n                      , Research report LA\u2010UR\u201095\u20103273, Los Alamos National Laboratory, Los Alamos, NM, 1995."},{"key":"R35","unstructured":"L. G. M. Reyna,\n                      Part III. On Composite Meshes\n                      , Ph.D. thesis, Department of Applied Mathematics, California Institute of Technology, Pasadena, CA, 1982."},{"key":"R36","doi-asserted-by":"publisher","DOI":"10.1115\/1.1436090"},{"key":"R37","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827598343826"},{"key":"R38","doi-asserted-by":"publisher","DOI":"10.1109\/8.997982"},{"key":"R39","doi-asserted-by":"publisher","DOI":"10.1137\/0908026"},{"key":"R40","unstructured":"A. Sussman, G. Agrawal, and J. Saltz,\n                      A Manual for the Multiblock PARTI Runtime Primitives, Revision 4.1\n                      , Technical report CS\u2010TR\u20103070.1, Department of Computer Science, University of Maryland, College Park, MD, 1993."},{"key":"R41","unstructured":"A. Taflove and S. C. Hagness,\n                      Computational Electrodynamics: The Finite\u2010Difference Time\u2010Domain Method\n                      , Artech House, Boston, 2000."},{"key":"R42","doi-asserted-by":"crossref","unstructured":"H. van de Hulst,\n                      Light Scattering by Small Particles\n                      , Dover, New York, 1957.","DOI":"10.1063\/1.3060205"},{"key":"R43","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1997.5686"},{"key":"R44","doi-asserted-by":"publisher","DOI":"10.1109\/TAP.1966.1138693"},{"key":"R45","doi-asserted-by":"publisher","DOI":"10.1109\/8.166532"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/050644379","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:55:10Z","timestamp":1787334910000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/050644379"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,1]]},"references-count":45,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2006,1]]}},"alternative-id":["10.1137\/050644379"],"URL":"https:\/\/doi.org\/10.1137\/050644379","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,1]]}}}