TDIE implementations have come a long way since their initial unstable first steps and are well on their way to becoming a fourth set of canonical methods in the computational electromagnetics toolbox. Five basic methods for temporal discretization have shown promise for the stable and accurate temporal discretization of TDIEs, and several fast methods have been concocted to improve their performances. While new applications of TDIEs are likely to continue pouring in, multiphysics and electromagnetic physics appear to be the short-term trajectory of these newest computational electromagnetics methods. Despite their unimpressive origins, TDIEs are finally poised to become a very new trend in computational electromagnetics.

Chapter Contents:

• 5.1 Introduction
• 5.1.1 A short history of TDIEs in electromagnetics
• 5.1.2 Time-domain integral equations and their discretization
• 5.2 Methods for the discretization of TDIEs
• 5.2.1 Exact integration
• 5.2.2 Band-limited interpolation and extrapolation
• 5.2.3 Laguerre basis
• 5.2.4 Series expansion
• 5.2.5 Convolution quadrature
• 5.3 Fast methods
• 5.3.1 Adaptive integral method
• 5.3.2 Plane-wave time-domain method
• 5.4 New trends in the solution of TDIEs
• 5.4.1 Multiphysics
• 5.4.2 Electromagnetic compatibility/interference
• 5.4.3 Stability enhancement
• 5.5 Conclusions
• References

Inspec keywords: electric field integral equations; computational electromagnetics; magnetic field integral equations; time-domain analysis

Other keywords: electromagnetic physics; time-domain integral equations; temporal discretization; TDIE; computational electromagnetics toolbox; multiphysics

Subjects: Integral equations (numerical analysis); Function theory, analysis; Classical electromagnetism; Electric and magnetic fields; Mathematical analysis