Advisor(s)

Carey M. Rappaport

Contributor(s)

Michael B. Silevitch, Jose Angel Martinez-Lorenzo

Date of Award

2007

Date Accepted

12-2007

Degree Grantor

Northeastern University

Degree Level

M.S.

Degree Name

Master of Science

Department or Academic Unit

College of Engineering. Department of Electrical and Computer Engineering.

Keywords

Loss mapped perfectly matched layer, Electrical engineering, Finite-difference time-domain, FDTD

Subject Categories

Lattice theory, Electromagnetic fields--Mathematical models

Disciplines

Engineering

Abstract

This thesis presents a loss mapped perfectly matched layer (LMPML) absorbing boundary conditions (ABC) for the truncation of finite-difference time-domain (FDTD) lattices. FDTD is one of the most popular computational techniques in today's electromagnetic field. While the FDTD is a well established, fairly accurate and easy-to-implement method within the computational grid, the truncation of the FDTD lattices is one of the most challenging parts of its implementation. Many methods of absorbing boundary conditions were proposed in the past few decades. Most of the earlier ABC proposals had only limited success in the reduction of the truncation error with the reflection as big as 1% of incident wave coming back into the computational grid. The revolution in the area occurred with the introduction of perfectly matched layer (PML) ABC formulated by Berenger. This formulation assures theoretical zero reflection for all frequencies and angles of incidence. But the practical implementation of the PML ABC has some inaccuracy due to the numerical discretization error. After the original PML ABC proposal many new works were published with the emphasis on improvement of the numerical results, interpretation of PML ABC into different coordinate systems and new more memory efficient formulations of PML ABC. This thesis concentrates on the development in the area of absorbing boundary conditions, discusses most popular methods before and after introduction of PML ABC and presents a new formulation of PML ABC. The new LMPML ABC formulation demonstrates the same level of absorption as original Berenger's method but is more memory efficient than the original formulation, at least for three-dimensional case. The proposed LMPML equations resemble Maxwellian formulation and regular wave equation which is a significant advantage of this technique.

Document Type

Master's Thesis

Rights Holder

Roman Trogan


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