An enhanced augmented electric field integral equation and the calculation of casimir force using computational electromagnetics

Xia, Tian

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https://hdl.handle.net/2142/101645 Copy

Description

Title

An enhanced augmented electric field integral equation and the calculation of casimir force using computational electromagnetics

Author(s)

Xia, Tian

Issue Date

2018-05-29

Director of Research (if dissertation) or Advisor (if thesis)

Chew, Weng Cho

Doctoral Committee Chair(s)

Chew, Weng Cho

Committee Member(s)

• Jin, Jianming
• Popescu, Gabriel
• Schutt-Ainé, José

Department of Study

Electrical & Computer Eng

Discipline

Electrical & Computer Engr

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

Integral equation, low frequency, fast algorithm, fast multipole algorithm, Casimir force.

Abstract

In this dissertation, a surface integral equation formulation is developed for low-frequency problems by generalizing the existing augmented electric field integral equation from the perfect electric conductors to the dielectrics and general conductors. Detailed discussions of the basis functions and the pre-conditioner are provided for the dielectric problems, and a novel integration scheme for the evaluations of the matrix elements in the conductor problem is proposed. Then a broadband multilevel fast multipole algorithm (FMA) using a hybridization of the multipole and plane wave expansions is introduced. This high-accuracy algorithm is error controllable and stable at low frequencies. It reduces to the conventional diagonal FMA at higher frequencies. Therefore it can be regarded as a generalization of the dense FMA at low frequencies and the diagonal FMA at higher frequencies. Finally, the computational electromagnetic techniques are applied to the calculations of the Casimir force. The application of the integral equation method in Casimir force calculation is briefly reviewed and we proposed an efficient computing scheme using the randomized singular value decomposition and the hybrid FMA. As a result, the efficiency can be greatly enhanced for large problems.

Graduation Semester

2018-08

Type of Resource

text

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http://hdl.handle.net/2142/101645

Copyright and License Information

Copyright 2018 Tian Xia

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