TY - JOUR

T1 - An Explicit Time Marching Scheme for Efficient Solution of the Magnetic Field Integral Equation at Low Frequencies

AU - Chen, Rui

AU - Sayed, Sadeed B

AU - Ulku, H. Arda

AU - Bagci, Hakan

N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): 2016-CRG5-2953
Acknowledgements: This work was supported by the King Abdullah University of Science and Technology (KAUST) Office of Sponsored Research (OSR) under Award No 2016-CRG5-2953.

PY - 2020

Y1 - 2020

N2 - An explicit marching-on-in-time (MOT) scheme to efficiently solve the time domain magnetic field integral equation (TD-MFIE) with a large time step size (under a low-frequency excitation) is developed. The proposed scheme spatially expands the current using high-order nodal functions defined on curvilinear triangles discretizing the scatterer surface. Applying Nyström discretization, which uses this expansion, to the TD-MFIE, which is written as an ordinary differential equation (ODE) by separating self-term contribution, yields a system of ODEs in unknown time-dependent expansion coefficients. A predictor-corrector method is used to integrate this system for samples of these coefficients. Since the Gram matrix arising from the Nyström discretization is blockdiagonal, the resulting MOT scheme replaces the matrix “inversion” required at each time step by a product of the inverse block-diagonal Gram matrix and the right-hand side vector. It is shown that, upon convergence of the corrector updates, this explicit MOT scheme produces the same solution as its implicit counterpart, and is faster for large time step sizes.

AB - An explicit marching-on-in-time (MOT) scheme to efficiently solve the time domain magnetic field integral equation (TD-MFIE) with a large time step size (under a low-frequency excitation) is developed. The proposed scheme spatially expands the current using high-order nodal functions defined on curvilinear triangles discretizing the scatterer surface. Applying Nyström discretization, which uses this expansion, to the TD-MFIE, which is written as an ordinary differential equation (ODE) by separating self-term contribution, yields a system of ODEs in unknown time-dependent expansion coefficients. A predictor-corrector method is used to integrate this system for samples of these coefficients. Since the Gram matrix arising from the Nyström discretization is blockdiagonal, the resulting MOT scheme replaces the matrix “inversion” required at each time step by a product of the inverse block-diagonal Gram matrix and the right-hand side vector. It is shown that, upon convergence of the corrector updates, this explicit MOT scheme produces the same solution as its implicit counterpart, and is faster for large time step sizes.

UR - http://hdl.handle.net/10754/664444

UR - https://ieeexplore.ieee.org/document/9149799/

U2 - 10.1109/TAP.2020.3010997

DO - 10.1109/TAP.2020.3010997

M3 - Article

SN - 1558-2221

SP - 1

EP - 1

JO - IEEE Transactions on Antennas and Propagation

JF - IEEE Transactions on Antennas and Propagation

ER -