A higher order space-time Galerkin scheme for time domain integral equations
AuthorsPray, Andrew J.
Nair, Naveen V.
KAUST DepartmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Electrical Engineering Program
Computational Electromagnetics Laboratory
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AbstractStability of time domain integral equation (TDIE) solvers has remained an elusive goal formany years. Advancement of this research has largely progressed on four fronts: 1) Exact integration, 2) Lubich quadrature, 3) smooth temporal basis functions, and 4) space-time separation of convolutions with the retarded potential. The latter method's efficacy in stabilizing solutions to the time domain electric field integral equation (TD-EFIE) was previously reported for first-order surface descriptions (flat elements) and zeroth-order functions as the temporal basis. In this work, we develop the methodology necessary to extend the scheme to higher order surface descriptions as well as to enable its use with higher order basis functions in both space and time. These basis functions are then used in a space-time Galerkin framework. A number of results are presented that demonstrate convergence in time. The viability of the space-time separation method in producing stable results is demonstrated experimentally for these examples.
SponsorsThis work was supported in part by the NSFunder Grant CCF1018516 and in part by the DoD SMART Program under Grant N00244-09-1-0081.