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

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Electrical & Computer Engr

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2018

Author dc:creator

• Xia, Tian

Contributors dc:contributor

• Chew, Weng Cho
• Jin, Jianming
• Popescu, Gabriel
• Schutt-Ainé, José

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

Statement dc:rights

• Copyright 2018 Tian Xia

Language dc:language

en

Handle dc:identifier

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

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/101645