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A butterfly‐based direct solver using hierarchical LU factorization for Poggio‐Miller‐Chang‐Harrington‐Wu‐Tsai equations
dc.contributor.authorGuo, Han
dc.contributor.authorLiu, Yang
dc.contributor.authorHu, Jun
dc.contributor.authorMichielssen, Eric
dc.date.accessioned2018-05-15T20:14:02Z
dc.date.available2019-08-01T19:53:23Zen
dc.date.issued2018-06
dc.identifier.citationGuo, Han; Liu, Yang; Hu, Jun; Michielssen, Eric (2018). "A butterfly‐based direct solver using hierarchical LU factorization for Poggio‐Miller‐Chang‐Harrington‐Wu‐Tsai equations." Microwave and Optical Technology Letters 60(6): 1381-1387.
dc.identifier.issn0895-2477
dc.identifier.issn1098-2760
dc.identifier.urihttps://hdl.handle.net/2027.42/143676
dc.description.abstractA butterfly‐based hierarchical LU factorization scheme for solving the PMCHWT equations for analyzing scattering from homogenous dielectric objects is presented. The proposed solver judiciously re‐orders the discretized integral operator and butterfly‐compresses blocks in the operator and its LU factors. The observed memory and CPU complexities scale as O(N log2 N) and O(N1.5 log N), respectively. The proposed solver is applied to the analyses of scattering several large‐scale dielectric objects.
dc.publisherWiley Periodicals, Inc.
dc.subject.otherintegral equation
dc.subject.otherscattering analysis
dc.subject.otherbutterfly scheme
dc.subject.otherPoggio‐Miller‐Chang‐Harrington‐Wu‐Tsai equation (PMCHWT)
dc.subject.otherhomogenous dielectrics
dc.subject.otherfast direct solver
dc.titleA butterfly‐based direct solver using hierarchical LU factorization for Poggio‐Miller‐Chang‐Harrington‐Wu‐Tsai equations
dc.typeArticleen_US
dc.rights.robotsIndexNoFollow
dc.subject.hlbsecondlevelElectrical Engineering
dc.subject.hlbtoplevelEngineering
dc.description.peerreviewedPeer Reviewed
dc.description.bitstreamurlhttps://deepblue.lib.umich.edu/bitstream/2027.42/143676/1/mop31166.pdf
dc.description.bitstreamurlhttps://deepblue.lib.umich.edu/bitstream/2027.42/143676/2/mop31166_am.pdf
dc.identifier.doi10.1002/mop.31166
dc.identifier.sourceMicrowave and Optical Technology Letters
dc.identifier.citedreferenceO’neil M, Woolfe F, Rokhlin V. An algorithm for the rapid evaluation of special function transforms. Appl Comput Harmon Anal. 2010; 28: 203 – 226.
dc.identifier.citedreferenceYla‐Oijala P, Taskinen M, Jarvenpaa S. Analysis of surface integral equations in electromagnetic scattering and radiation problems. Eng Anal Bound Elem. 2008; 32: 196 – 209.
dc.identifier.citedreferenceSong J, Lu C‐C, Chew WC. Multilevel fast multipole algorithm for electromagnetic scattering by large complex objects. IEEE Trans Antennas Propag. 1997; 45: 1488 – 1493.
dc.identifier.citedreferenceBebendorf M. Hierarchical LU decomposition‐based preconditioners for BEM. Computing. 2005; 74 ( 3 ): 225 – 247.
dc.identifier.citedreferenceShaeffer J. Direct solve of electrically large integral equations for problem sizes to 1 M unknowns. IEEE Trans Antennas Propag. 2008; 56: 2306 – 2313.
dc.identifier.citedreferenceChai W, Jiao D. An‐matrix‐based integral‐equation solver of reduced complexity and controlled accuracy for solving electrodynamic problems. IEEE Trans Antennas Propag. 2009; 57: 3147 – 3159.
dc.identifier.citedreferenceGreengard L, Gueyffier D, Martinsson P‐G, Rokhlin V. Fast direct solvers for integral equations in complex three‐dimensional domains. Acta Numerica. 2009; 18: 243 – 275.
dc.identifier.citedreferenceHeldring A, Rius JM, Tamayo JM, Parron J, Ubeda E. Multiscale compressed block decomposition for fast direct solution of method of moments linear system. IEEE Trans Antennas Propag. 2011; 59: 526 – 536.
dc.identifier.citedreferenceGuo H, Hu J, Shao H, Nie Z. Hierarchical matrices method and its application in electromagnetic integral equations. Int J Antennas Propag. 2012; 2012: 1.
dc.identifier.citedreferenceWei J‐G, Peng Z, Lee J‐F. A fast direct matrix solver for surface integral equation methods for electromagnetic wave scattering from non‐penetrable targets. Radio Sci. 2012; 47 ( 5 ).
dc.identifier.citedreferenceCorona E, Martinsson P‐G, Zorin D. An O(N) direct solver for integral equations on the plane. Appl Comput Harmon Anal. 2015; 38: 284 – 317.
dc.identifier.citedreferenceMichielssen E, Boag A, Chew W. Scattering from elongated objects: direct solution in O(N log 2 N) operations. IEE Proc Microw Antennas Propag. 1996; 143 ( 4 ): 277 – 283.
dc.identifier.citedreferenceMartinsson P‐G, Rokhlin V. A fast direct solver for scattering problems involving elongated structures. J Comput Phys. 2007; 221: 288 – 302.
dc.identifier.citedreferenceWinebrand E, Boag A. A multilevel fast direct solver for EM scattering from quasi‐planar objects. Proc Int Conf Electromagn Adv Appl IEEE. 2009; 640 – 643.
dc.identifier.citedreferenceBrick Y, Lomakin V, Boag A. Fast direct solver for essentially convex scatterers using multilevel non‐uniform grids. IEEE Trans Antennas Propag. 2014; 62: 4314 – 4324.
dc.identifier.citedreferenceMichielssen E, Boag A. A multilevel matrix decomposition algorithm for analyzing scattering from large structures. IEEE Trans Antennas Propag. 1996; 44: 1086 – 1093.
dc.identifier.citedreferenceCandes E, Demanet L, Ying L. A fast butterfly algorithm for the computation of Fourier integral operators. Multiscale Model Simul. 2009; 7: 1727 – 1750.
dc.identifier.citedreferenceTygert M. Fast algorithms for spherical harmonic expansions, III. J Comput Phys. 2010; 229: 6181 – 6192.
dc.identifier.citedreferenceLiu Y, Guo H, Michielssen E. A HSS matrix‐inspired butterfly‐based direct solver for analyzing scattering from two‐dimensional objects. IEEE Antennas Wirel Propag Lett. 2016.
dc.identifier.citedreferenceGuo H, Hu J, Michielssen E. On MLMDA/butterfly compressibility of inverse integral operators. IEEE Antennas Wirel Propag Lett. 2013; 12: 31 – 34.
dc.identifier.citedreferenceGuo H, Liu Y, Hu J, Michielssen E. A butterfly‐based direct integral equation solver using hierarchical LU factorization for analyzing scattering from electrically large conducting objects. IEEE Trans Antennas Propag. 2016; 65: 4742 – 4750.
dc.identifier.citedreferenceRao SM, Wilton DR, Glisson AW. Electromagnetic scattering by surfaces of arbitrary shape. IEEE Trans Antennas Propag. 1982; 30: 409 – 418.
dc.identifier.citedreferenceBucci OM, Franceschetti G. On the degrees of freedom of scattered fields. IEEE Trans Antennas Propag. 1989; 37: 918 – 926.
dc.owningcollnameInterdisciplinary and Peer-Reviewed


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