Time-domain single-source integral equations for analyzing scattering from homogeneous penetrable objects
KAUST DepartmentPhysical Sciences and Engineering (PSE) Division
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Electrical Engineering Program
Computational Electromagnetics Laboratory
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AbstractSingle-source time-domain electric-and magnetic-field integral equations for analyzing scattering from homogeneous penetrable objects are presented. Their temporal discretization is effected by using shifted piecewise polynomial temporal basis functions and a collocation testing procedure, thus allowing for a marching-on-in-time (MOT) solution scheme. Unlike dual-source formulations, single-source equations involve space-time domain operator products, for which spatial discretization techniques developed for standalone operators do not apply. Here, the spatial discretization of the single-source time-domain integral equations is achieved by using the high-order divergence-conforming basis functions developed by Graglia alongside the high-order divergence-and quasi curl-conforming (DQCC) basis functions of Valdés The combination of these two sets allows for a well-conditioned mapping from div-to curl-conforming function spaces that fully respects the space-mapping properties of the space-time operators involved. Numerical results corroborate the fact that the proposed procedure guarantees accuracy and stability of the MOT scheme. © 2012 IEEE.
SponsorsManuscript received February 17, 2012; revised June 15, 2012; accepted August 20, 2012. Date of publication November 15, 2012; date of current version February 27, 2013. This work was supported by the National Science Foundation under Grant DMS 0713771, the AFOSR/NSSEFF Program under Award FA9550-10-1-0180, Sandia under the Grant "Development of Calderon Multiplicative Preconditioners with Method of Moments Algorithms,", the Institut Mines-Telecom under the Grant "Futur et Ruptures CPCR11322," and KAUST uder Grant 399813.