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Partial differential equations

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Articles 31 - 38 of 38

Full-Text Articles in Applied Mathematics

Boundary Element Method (Bem) And Method Of Fundamental Solutions (Mfs) For The Boundary Value Problems Of The 2-D Laplace's Equation, Ermes Anthony Salgado-Ibarra Dec 2011

Boundary Element Method (Bem) And Method Of Fundamental Solutions (Mfs) For The Boundary Value Problems Of The 2-D Laplace's Equation, Ermes Anthony Salgado-Ibarra

UNLV Theses, Dissertations, Professional Papers, and Capstones

In this thesis we study the solution of the two dimensional Laplace equation by the boundary Element method (BEM) and the method of fundamental solutions (MFS). Both the BEM and MFS used to solve boundary value problems involving the Laplace equation 2-D settings. Both methods rely on the use of fundamental solution of the Laplace's equation (the solution of Laplace's equation in the distributional sense). We will contrast and compare the results we get using the BEM with results we get using the MFS.

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Source Optimization In Abstract Function Spaces For Maximizing Distinguishability: Applications To The Optical Tomography Inverse Problem, Bonnie Jacob May 2010

Source Optimization In Abstract Function Spaces For Maximizing Distinguishability: Applications To The Optical Tomography Inverse Problem, Bonnie Jacob

All Dissertations

The focus of this thesis is to formulate an optimal source problem for the medical imaging technique of optical tomography by maximizing certain distinguishability criteria. We extend the concept of distinguishability in electrical impedance tomography to the frequency-domain diffusion approximation model used in optical tomography.
We consider the dependence of the optimal source on the choice of appropriate function spaces, which can be chosen from certain Sobolev or Lp spaces. All of the spaces we consider are Hilbert spaces; we therefore exploit the inner product in several ways. First, we define and use throughout an inner product on the Sobolev …

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High Accuracy Multiscale Multigrid Computation For Partial Differential Equations, Yin Wang Jan 2010

High Accuracy Multiscale Multigrid Computation For Partial Differential Equations, Yin Wang

University of Kentucky Doctoral Dissertations

Scientific computing and computer simulation play an increasingly important role in scientific investigation and engineering designs, supplementing traditional experiments, such as in automotive crash studies, global climate change, ocean modeling, medical imaging, and nuclear weapons. The numerical simulation is much cheaper than experimentation for these application areas and it can be used as the third way of science discovery beyond the experimental and theoretical analysis. However, the increasing demand of high resolution solutions of the Partial Differential Equations (PDEs) with less computational time has increased the importance for researchers and engineers to come up with efficient and scalable computational techniques …

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The Derivation Of Hybridizable Discontinuous Galerkin Methods For Stokes Flow, Bernardo Cockburn, Jay Gopalakrishnan Jan 2009

The Derivation Of Hybridizable Discontinuous Galerkin Methods For Stokes Flow, Bernardo Cockburn, Jay Gopalakrishnan

Mathematics and Statistics Faculty Publications and Presentations

In this paper, we introduce a new class of discontinuous Galerkin methods for the Stokes equations. The main feature of these methods is that they can be implemented in an efficient way through a hybridization procedure which reduces the globally coupled unknowns to certain approximations on the element boundaries. We present four ways of hybridizing the methods, which differ by the choice of the globally coupled unknowns. Classical methods for the Stokes equations can be thought of as limiting cases of these new methods.

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Strings, Chains, And Ropes, Darryl H. Yong Nov 2006

Strings, Chains, And Ropes, Darryl H. Yong

All HMC Faculty Publications and Research

Following Antman [Amer. Math. Mon., 87 (1980), pp. 359–370], we advocate a more physically realistic and systematic derivation of the wave equation suitable for a typical undergraduate course in partial differential equations. To demonstrate the utility of this derivation, three applications that follow naturally are described: strings, hanging chains, and jump ropes.

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Quasioptimality Of Some Spectral Mixed Methods, Jay Gopalakrishnan, Leszek Demkowicz Jan 2004

Quasioptimality Of Some Spectral Mixed Methods, Jay Gopalakrishnan, Leszek Demkowicz

Mathematics and Statistics Faculty Publications and Presentations

In this paper, we construct a sequence of projectors into certain polynomial spaces satisfying a commuting diagram property with norm bounds independent of the polynomial degree. Using the projectors, we obtain quasioptimality of some spectralmixed methods, including the Raviart–Thomas method and mixed formulations of Maxwell equations. We also prove some discrete Friedrichs type inequalities involving curl.

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Dynamics And Control Of A Three Dimensional Gantry Crane With Cable Flexibility, Uchendu H. Eke Oct 1996

Dynamics And Control Of A Three Dimensional Gantry Crane With Cable Flexibility, Uchendu H. Eke

Mechanical & Aerospace Engineering Theses & Dissertations

The control of payload swing in industrial gantry cranes is a topic of widespread interest. In this thesis, the control of the swing of a payload idealized by a point mass assumption is investigated utilizing s, compact robotics matrix/vector representation of the dynamical model. In this form, this particular system can be viewed as sn underactuated manipulator with equal numbers of active and passive degrees of freedom. The full three dimensional model is developed and linearized by modelling the cable as a single thread of fiexible wire and the degree of dynamic coupling between the active and passive coordinates is …

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On Weakly Coupled Hyperbolic And Parabolic Partial Differential Equations Arising In Chemical Engineering Problems, Zhifeng Zhang May 1987

On Weakly Coupled Hyperbolic And Parabolic Partial Differential Equations Arising In Chemical Engineering Problems, Zhifeng Zhang

Theses

Many of the mathematical models arising in dynamical chemical processes are systems of weakly coupled hyperbolic and parabolic partial differential equations with constant coefficients. It is shown in this paper that this kind of systems of partial differential equations can be treated using generalizations of Green's functions. The Green's function is completely defined, including all boundary conditions, for systems with nonselfadjoint operators as well as those which are selfadjoint. The Green's functions can be expressed in terms of eigenvalues and eigenfunctions of the operator and the adjoint operator when they can be obtained. We develop a method based on higher …

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