• Innovative Solution of a 2-D Elastic Transmission Problem 

  Hsiao, George C.; Nigam, Nilima; Sändig, Anna-Margarete (2006-07-12)

  This paper is concerned with a boundary-field equation approach to a class of boundary value problems exterior to a thin domain. A prototype of this kind of problems is the interaction problem with a thin elastic structure. ...
• A Newton-Imbedding Procedure for Solutions of Semilinear Boundary Value Problems in Sobolev Spaces 

  Hsiao, G.C. (2006-07-12)

  This paper is concerned with the application of the Newton-imbedding iteration procedure to nonlinear boundary value problems in Sobolev spaces. A simple model problem for the second-order semilinear elliptic equations ...
• An Initial-Boundary Value Problem for the Viscous Compressible Flow 

  Hebeker, Friedrich-Karl; Hsiao, George C (2006-07-07)

  A constructive approach is presented to treat an initial boundary value problem for isothermal Navier Stokes equations. It is based on a characteristics (Lagrangean) approximation locally in time and a boundary intergral ...
• On the Boundary Integral Equation Method for a Mixed Boundary Value Problem of the Biharmonic Equation 

  Cakoni, F.; Hsiao, G.C.; Wendland, W. (Department of Mathematical Sciences, 2005)
• Flow of a Model for Dilute Wormlike Micellar Solutions 

  Rossi, L.F.; McKinley, G.; Cook, L.P (Depatment of Mathematical Sciences, 2006)
• Evaluation of the biot-savart integral for deformable elliptical gaussian vortex elements 

  Rossi, Louis F. (Mathematical Sciences Department, 2005)

  This paper introduces two techniques for approximating the Biot-Savart integral for deforming elliptical Gaussian functions. The primary motivation is to develop a high spatial accuracy vortex method. The first technique ...
• On pathwise uniqueness for stochastic heat equations with non-Lipschitz coefficients 

  Mytnik, Leonid; Perkins, Edwin; Sturm, Anja (Department of Mathematical Sciences, 2005-02-28)

  We consider the existence and pathwise uniqueness of the stochastic heat equation with a multiplicative colored noise term on R d for d greater than or equal to 1. We focus on the case of non-Lipschitz noise coefficients ...
• 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 ...
• A mathematical and experimental study of ant foraging line dynamics 

  Rossi, Louis F.; Johnson, Katie (Department of Mathematical Sciences, 2005-04-13)

  In this article, we present a mathematical model coupled to an experimental study of ant foraging lines. Our laboratory experiments do not support the common traffic modeling assumption that ant densities and velocities ...
• Eigenvalue stability of radial basis function discretizations for time-dependent problems 

  Platte, R.B.; Driscoll, Tobin A. (Department of Mathematical Sciences, 2005)

  Differentiation matrices obtained with infinitely smooth radial basis function (RBF) collo- cation methods have, under many conditions, eigenvalues with positive real part, preventing the use of such methods for ...
• 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 ...
• 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 ...
• 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 ...
• 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 ...
• 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 ...
• 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 ...
• 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 ...
• A High Order Langrangian Scheme for Flow Through Unsaturated Porous Media 

  Rossi, Louis F. (2001)

  A new high order Lagrangian method uses moving basis functions to represent the moisture content in an unsaturated porous material. The basis functions are localized elliptical Gaussians that can move, spread, elongate ...
• Bounded Film Evolution with Nonlinear Surface Properties 

  Debisschop, C.A.; Braun, Richard J.; Snow, S.A. (Department of Mathematical Sciences, 2001-09-12)

  We study the evolution of a Newtonian free surface of a thin film above a solid wall. We consider the case in which the horizontal solid is covered by a non-wetting fluid and an insoluble monolayer of surfactant is present ...

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