Thesis--Bonn. / Extra t.p. with thesis statement. Includes bibliographical references (p. 68-69).

Thesis (Ph. D.)--University of Washington, 1993. / Vita. Includes bibliographical references (leaves [54]-55).

Thesis (Ph.D.)--Baylor University, 2007. / Includes bibliographical references (p. 117-122).

Thesis--Bonn. / Extra t.p. with thesis statement. Includes bibliographical references (p. 68-69).

<p>A method is developed for solving the two dimensional Helmholtz equation in a ductwith varying cross-section region bounded by a curved top and flat bottom, having oneregion inside. To compute the propagation of sound waves in a curved duct with a curvedinternal interface is difficult problem. One method is to transform the wave equation intoa solvable form and making the curved interface plane. To this end a local orthogonaltransformation is developed for the varying cross-sectional duct having one medium inside.This transformation is first used to make the curved top of the waveguide flat andto transform the Helmholtz equation into an initial value problem. Later on the local orthogonaltransformation is developed for a waveguide having two media inside with flattop, a flat bottom and a curved interface. This local orthogonal transformation is used toflatten the interface and also to transform the Helmholtz equation into a simple, solvableordinary differential equation. In this paper we present operator formulation for the partwith flat bottom and curved top including a curved interface. In the ordinary differentialequation with operators in coefficients, obtained after the transformation, all the operationsrelated to the transverse variable are treated as operators while the derivative withrespect to the range variable is kept.</p>

A method is developed for solving the two dimensional Helmholtz equation in a ductwith varying cross-section region bounded by a curved top and flat bottom, having oneregion inside. To compute the propagation of sound waves in a curved duct with a curvedinternal interface is difficult problem. One method is to transform the wave equation intoa solvable form and making the curved interface plane. To this end a local orthogonaltransformation is developed for the varying cross-sectional duct having one medium inside.This transformation is first used to make the curved top of the waveguide flat andto transform the Helmholtz equation into an initial value problem. Later on the local orthogonaltransformation is developed for a waveguide having two media inside with flattop, a flat bottom and a curved interface. This local orthogonal transformation is used toflatten the interface and also to transform the Helmholtz equation into a simple, solvableordinary differential equation. In this paper we present operator formulation for the partwith flat bottom and curved top including a curved interface. In the ordinary differentialequation with operators in coefficients, obtained after the transformation, all the operationsrelated to the transverse variable are treated as operators while the derivative withrespect to the range variable is kept.

In the modern world, because of increasing oil prices and the need to control greenhouse gas emission, a new interest in the production of electric cars is coming about. One of the products is a charging point for electric cars, at which electric cars can be recharged by a plug in cable. Usually people are required to pay for the electricity after recharging the electric cars. Today, the payment is handled by using SMS or through the parking system. There is now an opportunity, in cooperation with AES (the company with which we are working), to equip the pole with GPRS, and this requires development and maintenance of the antenna. The project will include data analysis of the problem, measurements and calculations. In this work, we are computing energy flow of the wave due to the location of the antenna inside the box. We need to do four steps. First, we take a set of points (determined by the computational mesh) that have the same distance from the antenna in the domain. Second, we calculate the angles between the ground and the points in the set. Third, we do an angle-energy plot, to analyse which angle can give the maximum energy. And last, we need to compare the maximum energy value of different position of the antenna. We are going to solve the problem in Matlab, based on the Maxwell equation and the Helmholtz equation, which is not time-dependent.

We consider computation of resonances in open systems and acoustic scattering problems. These problems are posed on an unbounded domain and domain truncation is required for the numerical computation. In this paper, a perfectly matched layer (PML) technique is proposed for computation of solutions to the unbounded domain problems. For resonance problems, resonance functions are characterized as improper eigenfunction (non-zero solutions of the eigenvalue problem which are not square integrable) of the Helmholtz equation on an unbounded domain. We shall see that the application of the spherical PML converts the resonance problem to a standard eigenvalue problem on the infinite domain. Then, the goal will be to approximate the eigenvalues first by replacing the infinite domain by a finite computational domain with a convenient boundary condition and second by applying finite elements to the truncated problem. As approximation of eigenvalues of problems on a bounded domain is classical [12], we will focus on the convergence of eigenvalues of the (continuous) PML truncated problem to those of the infinite PML problem. Also, it will be shown that the domain truncation does not produce spurious eigenvalues provided that the size of computational domain is sufficiently large. The spherical PML technique has been successfully applied for approximation of scattered waves [13]. We develop an analysis for the case of a Cartesian PML application to the acoustic scattering problem, i.e., solvability of infinite and truncated Cartesian PML scattering problems and convergence of the truncated Cartesian PML problem to the solution of the original solution in the physical region as the size of computational domain increases.

In this dissertation we describe a coordinate scaling technique for the numerical approximation of solutions to certain problems posed on unbounded domains in two and three dimensions. This technique amounts to introducing variable coefficients into the problem, which results in defining a solution coinciding with the solution to the original problem inside a bounded domain of interest and rapidly decaying outside of it. The decay of the solution to the modified problem allows us to truncate the problem to a bounded domain and subsequently solve the finite element approximation problem on a finite domain. The particular problems that we consider are exterior problems for the Laplace equation and the time-harmonic acoustic and elastic wave scattering problems. We introduce a real scaling change of variables for the Laplace equation and experimentally compare its performance to the performance of the existing alternative approaches for the numerical approximation of this problem. Proceeding from the real scaling transformation, we introduce a version of the perfectly matched layer (PML) absorbing boundary as a complex coordinate shift and apply it to the exterior Helmholtz (acoustic scattering) equation. We outline the analysis of the continuous PML problem, discuss the implementation of a numerical method for its approximation and present computational results illustrating its efficiency. We then discuss in detail the analysis of the elastic wave PML problem and its numerical discretiazation. We show that the continuous problem is well-posed for sufficiently large truncation domain, and the discrete problem is well-posed on the truncated domain for a sufficiently small PML damping parameter. We discuss ways of avoiding the latter restriction. Finally, we consider a new non-spherical scaling for the Laplace and Helmholtz equation. We present computational results with such scalings and conduct numerical experiments coupling real scaling with PML as means to increase the efficiency of the PML techniques, even if the damping parameters are small.

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