Explicit Time Marching Schemes for Solving the Magnetic Field Volume Integral Equation
KAUST DepartmentElectrical Engineering Program
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
KAUST Grant Number2016-CRG5-2953
Online Publication Date2019-10-31
Print Publication Date2020-03
Permanent link to this recordhttp://hdl.handle.net/10754/659957
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AbstractA method for constructing explicit marching-on-in-time (MOT) schemes to solve the time domain magnetic field volume integral equation (TD-MFVIE) on inhomogeneous dielectric scatterers is proposed. The TD-MFVIE is cast in the form of an ordinary differential equation (ODE) and the unknown magnetic field is expanded using curl conforming spatial basis functions. Inserting this expansion into the TD-MFVIE and spatially testing the resulting equation yield an ODE system with a Gram matrix. This system is integrated in time for the unknown time-dependent expansion coefficients using a linear multistep method. The Gram matrix is sparse and well-conditioned for Galerkin testing and consists of only four diagonal blocks for point testing. The resulting explicit MOT schemes, which call for the solution of this matrix system at every time step, are more efficient than their implicit counterparts, which call for inversion of a fuller matrix system at lower frequencies. Numerical results compare the efficiency, accuracy, and stability of the explicit MOT schemes and their implicit counterparts for low-frequency excitations. The results show that the explicit MOT scheme with point testing is significantly faster than the other three solvers without sacrificing from accuracy.
CitationSayed, S. B., Ulku, H. A., & Bagci, H. (2019). Explicit Time Marching Schemes for Solving the Magnetic Field Volume Integral Equation. IEEE Transactions on Antennas and Propagation, 1–1. doi:10.1109/tap.2019.2949381
SponsorsThis publication is based upon work supported by the King Abdullah University of Science and Technology (KAUST) Office of Sponsored Research (OSR) under Award No 2016-CRG5-2953. The authors would like to thank the KAUST Supercomputing Laboratory (KSL) for providing the required computational resources.