An explicit marching on-in-time solver for the time domain volume magnetic field integral equation

Summary form only given. Transient scattering from inhomogeneous dielectric objects can be modeled using time domain volume integral equations (TDVIEs). TDVIEs are oftentimes solved using marching on-in-time (MOT) techniques. Classical MOT-TDVIE solvers expand the field induced on the scatterer using local spatio-temporal basis functions. Inserting this expansion into the TDVIE and testing the resulting equation in space and time yields a system of equations that is solved by time marching. Depending on the type of the basis and testing functions and the time step, the time marching scheme can be implicit (N. T. Gres, et al., Radio Sci., 36(3), 379-386, 2001) or explicit (A. Al-Jarro, et al., IEEE Trans. Antennas Propag., 60(11), 5203-5214, 2012). Implicit MOT schemes are known to be more stable and accurate. However, under low-frequency excitation, i.e., when the time step size is large, they call for inversion of a full matrix system at very time step.One can expect that an explicit scheme would be more efficient at low frequencies if it uses the same time step as its implicit counterpart while maintaining its stability and accuracy. Indeed, recently a novel explicit MOT solver, which satisfies this criterion, has been developed for solving the time domain surface magnetic field integral equation (H. A. Ulku, et al., IEEE Trans. Antennas Propag., 61(8), 4120-4131, 2013). In this work, this explicit MOT scheme is applied in solving the time domain volume magnetic field integral equation (TDVMFIE). The proposed solver expands the unknown fields using curl-conforming basis functions in space. Inserting this expansion into the TDVMFIE and using Galerkin testing yield a semi-discrete system of equations. This system is integrated in time using a predictor-corrector scheme (A. Glaser and V. Rokhlin, J. Sci. Comput., 38(3), 368-399, 2009) to obtain the coefficients of the expansion. The resulting scheme calls for inversion of a matrix system at every time step but this - an be carried out very efficiently since the pertinent Gram matrix is well conditioned and sparse regardless of the time step. The stability of the resulting MOT scheme is maintained using successive over relaxation (SOR) applied at the corrector step(S. B. Sayed, et al., Pr. Electromagn. Res. S., 378, Stockholm, 2013). Numerical results, which demonstrate that the proposed MOT-TDMVIE solver (i) uses time step as large as those of its implicit counterparts without sacrificing accuracy or stability, (ii) is faster than the implicit solver for low-frequency excitations, and (iii) maintains its efficiency, accuracy, and stability even when applied on high contrast scatterers, will be presented.