Plane -Wave Time -Domain Algorithms for Efficient Analysis of Three-Dimensional Transient Wave Phenomena
Ergin, Arif Ahmet
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https://hdl.handle.net/2142/81333
Description
Title
Plane -Wave Time -Domain Algorithms for Efficient Analysis of Three-Dimensional Transient Wave Phenomena
Author(s)
Ergin, Arif Ahmet
Issue Date
2000
Doctoral Committee Chair(s)
Eric Michielssen
Department of Study
Electrical Engineering
Discipline
Electrical Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Physics, Acoustics
Language
eng
Abstract
Computer simulation of linear transient wave phenomena involving structures that reside in an unbounded medium to generate broadband data is of paramount importance in such disciplines as acoustics, electromagnetics, and geophysics. Numerical techniques to perform such simulations call for the evaluation of retarded-time boundary integrals (RTBIs) as these boundary integrals play a fundamental role in formulation of the integral equation-based numerical techniques and in imposing exact radiation boundary conditions used in differential equation-based methods. However, evaluation of RTBIs using classical techniques is a computationally expensive procedure limiting the applicability of numerical transient analysis techniques to a small number of problems. In this thesis, numerical schemes for analyzing transient wave interactions with large-scale structures are introduced. Central to these techniques are the formulation of integral equations that are capable of producing stable and accurate results and the development of plane-wave time-domain (PWTD) algorithms for efficient evaluation of RTBIs. In the first part of this thesis, time domain combined field integral equations for analyzing acoustic and electromagnetic wave scattering are introduced and their superiority, in terms of accuracy and stability, to currently used integral equations is shown. In the second part, two PWTD algorithms based on Whittaker and finite-cone plane wave expansions of radiated fields are introduced. It is shown that the computational complexity of evaluating RTBIs can be considerably reduced by using these PWTD algorithms within a two-level or a multilevel framework. The last part of the thesis demonstrates the efficacy of using the resulting two-level and multilevel schemes both in integral equation-based transient scattering analysis from impenetrable obstacles and in imposing exact boundary conditions in the finite-difference time-domain technique. Numerous acoustic and electromagnetic examples are presented that show that the introduced schemes bring the transient analysis of wave scattering from realistic large-scale structures within the reach of current computational resources.
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