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Showing 1 to 20 of 36 for “"elliptic partial differential equations"”.
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Semilinear elliptic partial differential equations with the critical Sobolev exponent
… applied to solving certain types of semilinear elliptic partial differential equations (PDEs). The ultimate goal is to prove results on the existence and non-existence of solutions to the Semilinear Elliptic PDEs with the Critical Sobolev Exponent. To this end, we first recall some useful …
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Parallel algorithms and architectures for solving elliptic partial differential equations
Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1985.
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Comparison Theorems in Elliptic Partial Differential Equations with Neumann Boundary Conditions
<p>In this thesis, we study how the solution of a PDE changes when the data are rearranged. Specifically, we prove comparison theorems on spherical shells, spheres, and hemispheres, showing that under rearrangement of the data, the solution's convex mean increases. We also obtain similar weighted …
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Covolume-Upwind Finite Volume Approximations For Linear Elliptic Partial Differential Equations
… grids for solving second-order linear elliptic partial differential equations with mixed boundary conditions. This class of problems has intensive applications in various fields of science and engineering, e.g., fluid mechanics, groundwater prediction, environmental protection. An …
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Domain decomposition and high order discretization of elliptic partial differential equations
Numerical solutions of partial differential equations (PDEs) resulting from problems in both the engineering and natural sciences result in solving large sparse linear systems Au = b. The construction of such linear systems and their solutions using either direct or iterative methods are topics of …
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Modelling and Animation using Partial Differential Equations. Geometric modelling and computer animation of virtual characters using elliptic partial differential equations.
… and animation of parametric surfaces using elliptic Partial Differential Equations (PDE) which are produced via the PDE method. Compared with traditional surface generation techniques, the PDE method is an effective technique that can represent complex three-dimensional (3D) geometries in …
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Modelling and Animation using Partial Differential Equations. Geometric modelling and computer animation of virtual characters using elliptic partial differential equations.
… and animation of parametric surfaces using elliptic Partial Differential Equations (PDE) which are produced via the PDE method. Compared with traditional surface generation techniques, the PDE method is an effective technique that can represent complex three-dimensional (3D) geometries in …
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Estimates For Solutions Of Elliptic Partial Differential Equations With Explicit Constants And Aspects Of The Finite Element Method For Second-Order Equations
The classic Lp -based estimates for solutions of elliptic partial differential equations satisfying general boundary conditions were obtained by Agmon, Douglis, and Nirenberg in 1959. In Chapter 2, we rework these estimates to make their dependence on p explicit. It has long been believed that p …
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Reduced-basis methods applied to locally non-affine and locally non-linear partial differential equations
… a huge demand for solutions of parameter-based partial differential equations and associated outputs of interest expressed as functionals of these solutions. Areas that require solving partial differential equations include - but are not restricted to heat transfer, elasticity, and fluid …
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Convective mass transport for viscous flow past an evolving boundary
… developed that solves two-dimensional Helmholtz equations. This high order technique is shown to be adaptable to a variety of boundary conditions and solves elliptic partial differential equations efficiently such that it is applicable to moving boundary problems of arbitrarily shaped domains. A …
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Developments and extensions of Roth's method of double Fourier series with applications to the solution of electromagnetic field problems
… cosine transform method, for solving certain elliptic partial differential equations arising in practice. In particular we consider the solution of steady state problems associated with insulated conductors in rectangular slots. Roth's method has two main disadvantages namely the slow rate of …
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Row Projection Methods for Linear Systems
… (RP) methods for solving linear systems of equations are algorithms that require orthogonal projections onto the set of solutions of subsets of the equations. RP methods are categorized and their convergence properties summarized and extended. An implementation approach is presented for …
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Systems of Nonlinear Algebraic Equations Arising in Simulation of Semiconductor Devices
… we present several formulations of the system of elliptic partial differential equations that model a semiconductor device. We use standard finite difference methods to discretize these equations and derive systems of nonlinear equations. Due to the extremely large number of unknowns it is …
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Boundary Value Problems in Rectilinearly Anisotropic Thermoelastic Solids
… theory is employed, is governed by a set of elliptic partial differential equations. The general solution of these equations is expressed in terms of arbitrary analytic functions whose real parts, in turn, are expressed in terms of Fourier type integrals or Fourier series. Integral transform …
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An Efficient Parallel Three-Level Preconditioner for Linear Partial Differential Equations
… investigate parallel preconditioners for linear elliptic partial differential equations. Three preconditioners are studied: block-Jacobi preconditioner (BJ), a two-level tangential preconditioner (D0), and a three-level preconditioner (D1). Performance and scalability on a distributed memory …
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The analytic and asymptotic behaviors of vortices
"We study vortex equations with a parameter $s$ on smooth vector bundles $E$ over compact K\""ahler manifolds $M$. For each $s$, we invoke techniques in \cite{Br} by turning vortex equations into the elliptic partial differential equations considered in \cite{kw} and obtain a family of solutions. …
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Supercritical Semi-Linear Elliptic Problems Using Variational Principles
… the use of variational methods to study elliptic partial differential equations (PDEs) with supercritical nonlinearities. By focusing on convex subsets of a Banach space, the research overcomes compactness issues typically encountered with nonlinearities that exceed the Sobolev embedding …
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Adaptive Finite Element Methods for Optimization in Partial Differential Equations
… of optimal control problems governed by (elliptic) partial differential equations. The Lagrangian formalism yields the first-order necessary optimality condition in form of an indefinite boundary value problem which is approximated by an adaptive Galerkin finite element method. The mesh …
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Reduced basis approximation and a posteriori error estimation for non-coercive elliptic problems : applications to acoustics
… evaluation of which demands the solution of a partial differential equation. We present in this thesis a general methodology for the predicition of outputs of interest of non-coercive elliptic partial differential equations. The essential ingredients are: (i) rapidly convergent reduced basis …
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