A study on computational electromagnetics problems with applications to casimir force calculations

Atkins, Phillip

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https://hdl.handle.net/2142/46782 Copy

Description

Title

A study on computational electromagnetics problems with applications to casimir force calculations

Author(s)

Atkins, Phillip

Issue Date

2014-01-16T18:02:22Z

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

Chew, Weng Cho

Doctoral Committee Chair(s)

Chew, Weng Cho

Committee Member(s)

• Aluru, Narayana R.
• Jin, Jianming
• Kudeki, Erhan

Department of Study

Electrical and Computer Engineering

Discipline

Electrical and Computer Engineering

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• Electromagnetics
• Computational Electromagnetics
• Quantum Mechanics
• Casimir Force
• Method of Moments
• Domain Decomposition Method
• Fast Multipole Algorithm

Abstract

This work covers two main subjects, the efficient calculation of the dyadic Green's function for layered media (DGLM) and the calculation of the Casimir force using computational electromagnetics (CEM). The calculation of the DGLM is desirable for many problems that involve stratified media, like the cases of the subsurface of the earth and seabed, or circuits involving layers of substrates. The DGLM helps make the solving of these problems more efficient by allowing for the layered inhomogeneity to be incorporated into the Green's function. In this manner, we no longer need to explicitly model the background inhomogeneity. However, the calculation of the DGLM requires the evaluation of semi-infinite Sommerfeld integrals which prove to be a costly venture. An interpolation scheme is proposed here to allow for more efficient calculations of the Sommerfeld integrals. The interpolation is unique by its reuse of the same interpolation matrix to estimate the function and its derivatives that make up the DGLM. The Casimir force is an intermolecular force of recent interest due to up and coming micro-electromechanical systems (MEMS) devices. The Casimir force becomes relevant in the behavior of MEMS devices and efficient calculation of the forces would be desirable to aid in their design. Recent methods have been developed that incorporate CEM techniques, notably the electric field integral equation (EFIE). Herein, we present three methods, one of a new devising, that make use of various CEM techniques. Our new method allows for the easy incorporation of different techniques to address problems like low frequency breakdown, arbitrary materials, and domain decomposition methods (DDM). In addition, work on incorporating large scale techniques to increase the size of the problems is discussed.

Graduation Semester

2013-12

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http://hdl.handle.net/2142/46782

Copyright and License Information

Copyright 2013 Phillip R. Atkins

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