Timedomain methods are preferred over their frequencydomain counterparts for solving acoustic and electromagnetic scattering problems since they can produce wide band data from a single simulation. Among the timedomain methods, timedomain surface integral equation solvers have recently found widespread use because they offer several benefits over differential equation solvers.
This dissertation develops several secondkind surface integral equation solvers for analyzing transient acoustic scattering from rigid and penetrable objects and transient electromagnetic scattering from perfect electrically conducting and dielectric objects.
For acoustically rigid, perfect electrically conducting, and dielectric scatterers, fully explicit marchingonintime schemes are developed for solving time domain Kirchhoff, magnetic field, and scalar potential integral equations, respectively. The unknown quantity (e.g., velocity potential, electric current, or scalar potential) on the scatterer surface is discretized using a higherorder method in space and Lagrange interpolation in time. The resulting system is cast in the form of an ordinary differen tial equation and integrated in time using a predictorcorrector scheme to obtain the unknown expansion coefficients. The explicit scheme can use the same time step size as its implicit counterpart without sacrificing from the stability of the solution and is much faster under lowfrequency excitation (i.e., for large time step size). In addition, lowfrequency behavior of vector potential integral equations for perfect electrically conducting scatterers is also investigated in this dissertation.
For acoustically penetrable scatterers, presence of spurious interior resonance
modes in the solutions of two forms of time domain surface integral equations is investigated. Numerical results demonstrate that the solution of the form that is widely used in the literature is corrupted by the interior resonance modes. But, the amplitude of these modes in the time domain can be suppressed by increasing the accuracy of discretization especially in time. On the other hand, the proposed one in the combined form shows a resonancefree performance verified via numerical experiments.
In addition to providing detailed formulations of these solvers, the dissertation presents numerical examples, which demonstrate the solversâ€™ accuracy, efficiency, and applicability in reallife scenarios.
Date of Award  Apr 2021 

Original language  English (US) 

Awarding Institution   Computer, Electrical and Mathematical Science and Engineering


Supervisor  Hakan Bagci (Supervisor) 

 Acoustic Scattering
 Electromagnetic Scattering
 Explicit Solver
 Marchingonintime Scheme
 Surface Integral Equation
 Transient Analysis