Dissertation/Thesis Abstract

Numerical solutions of Maxwell's equations in 1D, 2D, and 3D via the finite element method
by Sahib, Sonny S., M.S., California State University, Long Beach, 2010, 98; 1493052
Abstract (Summary)

Index notation is used almost exclusively to define physical phenomenon in theoretical or physics-based journals. Unfortunately, it is nearly impossible to develop efficient computer algorithms for index notation; hence, most engineering software packages use matrix notation to solve real-world problems.

A novel method is introduced in which the index notation definition of electromagnetic fields is converted into matrix notation with special positioning. This formulation will allow existing field analysis software to calculate the effects of electromagnetic fields in one, two, and three dimensions.

Formulation of unique vector potentials from interacting fields will be defined. These potentials are required in order to convert Maxwell's equations into a system of partial differential equations and a set of boundary conditions. Additionally, the mass, damping, and stiffness matrices, as well as the associated excitations can be related to electromagnetic properties. The four degrees of freedom are partitioned in a vector {A} and a scalar ψ. This is important to solve special cases, such as electrostatics, magnetostatics, and steady currents. These equations can then be solved via standard numerical methods, such as Ritz, Galerkin, and virtual work.

A solid model of a linear synchronous motor used in maglev trains will be analyzed using FEKO electromagnetic field analysis software. This software utilizes the finite element method to solve the electrical and magnetic flux densities.

Indexing (document details)
Advisor: Ohtmer, Ortwin
School: California State University, Long Beach
School Location: United States -- California
Source: MAI 49/05M, Masters Abstracts International
Subjects: Mechanical engineering
Publication Number: 1493052
ISBN: 978-1-124-61475-5
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