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Browsing Math Technical Report Series by Issue Date

Now showing items 1-20 of 68

STABILITY OF VISCOELASTIC FILAMENTS: COMPARISON OF CONSTITUTIVE MODELS

Olagunju, David O. (Department of Mathematical Sciences, 1999-07-23)

A thin filament model is used to analyze the stability of a viscoelastic thread subject to uniaxial stretching. Linear stability analysis is carried out for a number of different constitutive models, namely the ...
Integral Representation in the Hodograph Plane for Compressible flow Problems

Hanson, E.B.; Hsiao, George C. (Department of Mathematical Sciences, 1999-12-07)

Compressible flow is considered in the hodograph plane. The fact that the equation for the stream function is linear there is exploited to derive a representation formula for the stream function, involving boundary data ...
Variational Methods for Boundary Integral Equations: Theory and Applications

Hsiao, George C. (Department of Mathematical Sciences, 1999-12-19)

Variational methods for boundary integral equations deal with the weak formulations of boundary integral equations. Their numerical discretizations are known as the boundary element methods. The later has become one of ...
Basis Properties of Traces and Normal Derivatives of Spherical-Separable Solutions of the Helmholtz Equation

Dallas, A.G. (Department of Mathematical Sciences, 2000)

The classical solutions of the Heimholtz equation resulting from the separation-of-variables procedure in spherical coördinates are frequently used in one way or another to approximate other solutions. In particular, traces ...
Recent Developments in Inverse Acoustic Scattering Theory

Colton, David; Coyle, J.; Monk, Peter B. (Department of Mathematical Sciences, 2000)

We survey some of the highlights of inverse scattering theory as it has developed over the past fifteen years, with emphasis on uniqueness theorems and reconstruction algorithms for time harmonic acoustic waves. Included ...
Finite Element Method for Approximating Electro-Magnetic Scattering from a Conducting Object

Kirsch, A.; Monk, Peter B. (Department of Mathematical Sciences, 2000)

We provide an error analysis of a fully discrete finite element – Fourier series method for approximating Maxwell’s equations. The problem is to approximate the electromagnetic field scattered by a bounded, inhomogeneous ...
Scattering of Time-Harmonic Electromagnetic Waves by Anisotropic Inhomongeneous Scatters or Impenetrable Obstacles

Monk, Peter B.; Coyle, J. (Department of Mathematical Sciences, 2000)

We investigate an overlapping solution technique to compute the scattering of time-harmonic electromagnetic waves in two dimensions. The technique can be used to compute waves scattered by penetrable anisotropic inhomogeneous ...
Boundary Integral Methods in Low Frequency Acoustics

Hsiao, George C.; Wendland, W.L. (Department of Mathematical Sciences, 2000)

This expository paper is concerned with the direct integral formulations for boundary value problems of the Helmholtz equation. We discuss unique solvability for the corresponding boundary integral equations and its ...
Mathematical Foundations for the Boundary-Field Equation Methods in Acoustic and Electromagnetic Scattering

Hsiao, George C. (Department of Mathematical Sciences, 2000)

The essence of the boundary-field equation method is the reduction of the boundary value problem under consideration to an equivalent nonlocal boundary value problem in a bounded domain by using boundary integral ...
Hybrid Coupled Finite-Boundary Element Methods for Elliptical Systems of Second Order

Hsiao, George C.; Schnack, E.; Wendland, W.L. (Department of Mathematical Sciences, 2000)

In this hybrid method, we consider, in addition to traditional finite elements, the Trefftz elements for which the governing equations of equilibrium are required to be satisfied a priori within the subdomain elements. ...
Toward the Direct Analytical Determination of the Pareto Optima of a Differentiable Mapping, I: Domains in Finite-Dimensional Spaces

Dallas, A.G. (Department of Mathematical Sciences, 2000)

The problem of locating the Pareto-optimal points of a differentiable mapping $F: {\mathcal M}^N \to {I\kern-.30em R}^n$ is studied, with the domain ${\cal M}^N$ a differentiable N-dimensional submanifold-without-boundary ...
On the Convergence and Numerical Stability of the Second Waterman Scheme for Approximation of the Acoustic Field Scattered by a Hard Object

Dallas, A.G. (Department of Mathematical Sciences, 2000)

The numerical schemes of P.C. Waterman (J. Acoust. Soc. Am.45 (1969), 1417-1429), frequently referred to under the name of "the T-Matrix method," have formed the basis for many scattering computations in many settings. ...
Accurate Discretisation of a Nonlinear Micromagnetic Problem

Monk, Peter B.; Vacus, O. (Department of Mathematical Sciences, 2000)

In this paper we propose a finite element discretization of the Maxwell-Landau-Lifchitz-Gilbert equations governing the electromagnetic field in a ferromagnetic material. Our point of view is that it is desirable for the ...
Domain Decomposition Methods via Boundary Integral Equations

Hsiao, George C.; Steinbach, O.; Wendland, W.L. (Department of Mathematical Sciences, 2000-12-21)

Domain decomposition methods are designed to deal with coupled or transmission problems for partial differential equations. Since the original boundary value problem is replaced by local problems in substructures, domain ...
Numerical Experiments with Isometric Mapping and Back-Projection for Conditioning Families in a Simple Sobolev Space

Dallas, A.G. (Department of Mathematical Sciences, 2001)

Numerically stable Galerkin procedures can be constructed by ensuring that the families of trial- and test-functions are well conditioned in the respective Hilbert spaces between which the operator is an (appropriate) ...
A Model for Anisotropic Epitaxial Lateral Overgrowth

Khenner, M.; Braun, Richard J.; Mauk, M.G. (Department of Mathematical Sciences, 2001)

The model for anisotropic crystal growth on a substrate covered by a mask material with a periodic series of parallel long trenches where the substrate is exposed to the vapor phase if developed. The model assumes that ...
A Model for Isotropic Crystal Growth from Vapor on a Patterned Substrate

Khenner, M.; Braun, Richard J.; Mauk, M.G. (Department of Mathematical Sciences, 2001)

We developed a consistent mathematical model for isotropic crystal growth on a substrate covered by the mask material with periodic series of parallel long trenches where the substrate is exposed to the vapor phase. Surface ...
Reformulating a Boundary-Integral Equation in Three Dimensions as as Integral-Operator Problem in a Plane Region

Dallas, A.G. (Department of Mathematical Sciences, 2001)

Motivated by a desire to simplify the design of numerically stable and efficient approximation schemes for boundary-operator problems, we develop a framework in which an integral equation on the boundary of a domain ...
High Order Vortex Methods With Deforming Elliptical Gaussian Blobs 1: Derivation and Validation

Rossi, Louis F. (Department of Mathematical Sciences, 2001)

This manuscript introduces a new vortex method based on elliptical Gaussian basis functions. Each basis function translates, nutates, elongates and spreads through the action of the local flow field and fluid viscosity. ...
On the Existence of Two-Dimensional, Localized, Rotating, Self-Similar Vortical Structures

Rossi, Louis F.; Graham-Eagle, J. (Department of Mathematical Sciences, 2001)

We prove that a Gaussian monopole, also known as the Lamb-Oseen vortex, is the only localized, rotating, self-similar solution to the two-dimensional, incompressible Navier-Stokes equations where level sets of vorticity ...

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