TY - CHAP

T1 - Explicit Marching-on-in-time Solvers for Second-kind Time Domain Integral Equations

AU - Chen, Rui

AU - Sayed, Sadeed B.

AU - Ulku, Huseyin A.

AU - Bagci, Hakan

N1 - KAUST Repository Item: Exported on 2022-11-30

PY - 2022/11/18

Y1 - 2022/11/18

N2 - Time domain methods are often preferred over their frequency domain counterparts for numerical electromagnetic analysis since they can produce broadband data from a single simulation, can account for nonlinearities directly, and often provide immediate physical interpretation of the problem's solution. Among the time domain methods, time domain integral equation (TDIE) solvers have recently found widespread use, and they have become an attractive alternative to differential equation solvers such as finite difference time domain schemes and time domain finite element method, especially for open region scattering problems. This is because TDIE solvers do not suffer from numerical phase dispersion, do not require approximate radiation boundary conditions (such as absorbing boundary conditions and perfectly matched layers), and their time step size is not restricted by a Courant–Friedrichs–Lewy-like condition. Almost all traditional TDIE solvers utilize an implicit time marching scheme, i.e. they call for solution of a (sparse) matrix at every iteration. This reduces the computational effciency under low-frequency excitations and makes the use of TDIE solvers in multiphysics frameworks a challenge. To address these challenges, recently, various explicit marching-on-in-time (MOT) schemes have been developed to solve the second kind TDIEs for perfect electrically conducting and dielectric scatterers. This chapter details the formulation and implementation of these TDIE solvers. These schemes cast the second kind TDIE in the form of an ordinary differential equation (ODE). A classical scheme such as those making use of Rao–Wilton–Glisson and Schubert–Wilton–Glisson basis functions and Nyström integration is used for spatial discretization. Then, a predictor-corrector scheme is used to integrate the spatially discretized ODE systems in time for the expansion coefficients of the unknowns. The explicit TDIE solvers described in this chapter use the same time step size as their implicit counterparts without sacrificing from accuracy and stability of the solution. In addition, they are significantly faster under low-frequency excitations. Numerical results are presented to demonstrate these computational benefits.

AB - Time domain methods are often preferred over their frequency domain counterparts for numerical electromagnetic analysis since they can produce broadband data from a single simulation, can account for nonlinearities directly, and often provide immediate physical interpretation of the problem's solution. Among the time domain methods, time domain integral equation (TDIE) solvers have recently found widespread use, and they have become an attractive alternative to differential equation solvers such as finite difference time domain schemes and time domain finite element method, especially for open region scattering problems. This is because TDIE solvers do not suffer from numerical phase dispersion, do not require approximate radiation boundary conditions (such as absorbing boundary conditions and perfectly matched layers), and their time step size is not restricted by a Courant–Friedrichs–Lewy-like condition. Almost all traditional TDIE solvers utilize an implicit time marching scheme, i.e. they call for solution of a (sparse) matrix at every iteration. This reduces the computational effciency under low-frequency excitations and makes the use of TDIE solvers in multiphysics frameworks a challenge. To address these challenges, recently, various explicit marching-on-in-time (MOT) schemes have been developed to solve the second kind TDIEs for perfect electrically conducting and dielectric scatterers. This chapter details the formulation and implementation of these TDIE solvers. These schemes cast the second kind TDIE in the form of an ordinary differential equation (ODE). A classical scheme such as those making use of Rao–Wilton–Glisson and Schubert–Wilton–Glisson basis functions and Nyström integration is used for spatial discretization. Then, a predictor-corrector scheme is used to integrate the spatially discretized ODE systems in time for the expansion coefficients of the unknowns. The explicit TDIE solvers described in this chapter use the same time step size as their implicit counterparts without sacrificing from accuracy and stability of the solution. In addition, they are significantly faster under low-frequency excitations. Numerical results are presented to demonstrate these computational benefits.

UR - http://hdl.handle.net/10754/686005

UR - https://ieeexplore.ieee.org/document/9960943/

U2 - 10.1002/9781119808404.ch7

DO - 10.1002/9781119808404.ch7

M3 - Chapter

SN - 9781119808381

SP - 275

EP - 320

BT - Advances in Time‐Domain Computational Electromagnetic Methods

PB - IEEE

ER -