Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 15 of 15 for “"Elliptic PDE"”.
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Statistical inference and computation in elliptic PDE models
Partial differential equations (PDE) are ubiquitous in describing real-world phenomena. In many statistical models, PDE are used to encode complex relationships between unknown quantities and the observed data. We investigate statistical and computational questions arising in such models, adopting …
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Laplace's equation on perturbed domains
Laplace's equation is a prototypical elliptic PDE that appears in many electromagnetic and fluid dynamics problems. We develop two methods for solving Laplace's equation on domains that are perturbations of a circle. These methods are derived from governing equations and applied to several test …
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Maximal Graphs and Spacelike Mean Curvature Flows in Semi-Euclidean Spaces
… assumptions allow the application of standard elliptic PDE methods by providing sufficiently strong a priori gradient estimates. The second result is a version of Brian White’s local regularity theorem, but now for the spacelike mean curvature flow system in semi-Euclidean spaces. This is …
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The evolution equation for closed magnetic geodesics
… As generalization one can consider a system of elliptic nonlinear partial differential equations whose solutions describe the orbits of closed p-branes under the effect of a "generalized physical force". For the corresponding evolution equation, which is a system of parabolic nonlinear partial …
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Travelling wave solutions of the heat equation in an unbounded cylinder with a non-linear boundary condition
… Finding such a solution amounts to solving the elliptic PDE $Delta u - c partial_x u = 0$ for $(x,y)inRimesOmega$ with $partial u over partial n = f(u)$ on $RimespartialOmega$. The main result is the existence of a non-trivial solution of this equation for a large class of non-linearities $f$. …
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Numerical solution and spectrum of boundary-domain integral equations
… Dirichlet boundary value problem for a scalar elliptic PDE with variable coefficient is discussed in this thesis. The BDIE and LBDIE related to Neumann problem are reduced to a uniquely solvable one by adding an appropriate perturbation operator. The mesh-based discretisation of the BDIE/BDIDEs …
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Analytic Solutions to the Laplace, Poisson, and Biharmonic Equations with Internal Boundaries: Theory and Application to Microfluidic Dynamics
… focuses on developing analytical methods for elliptic partial differential equations with conditions imposed on internal boundaries. Internal boundaries are formed where materials with different properties meet to form interfaces. These interfaces arise in a variety of physical and engineering …
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Geometric Computing beyond the Laplacian
… computing algorithms built on operators or PDEs other than the ordinary Laplacian. Borrowing insights from optimal control and inverse PDE problems, we propose efficient numerical schemes to search for the metric or conformal structure whose associated (generalized) Laplacian is optimal for …
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Towards Coupled Nonhydrostatic-Hydrostatic Hybridizable Discontinuous Galerkin Method
… models arises from solving a globally coupled elliptic PDE for the NHS pressure. Optimally reducing these costs such that the NHS dynamics are resolved where needed is the motivation for this work. We propose a new multi-dynamics model to decompose a domain into NHS and HS dynamic regions and …
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On two-valued minimal graphs and minimal surfaces arising from the Allen-Cahn equation
… deals with minimal arising from a semilinear elliptic PDE called the Allen-Cahn equation. There we prove a spectral lower bound for hypersurfaces that arise from sequences of critical points with bounded indices. In particular, the index of two-sided minimal hypersurfaces constructed using …
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SPDE-derived random fields in structural optimisation and elastodynamics
… and stochastic partial differential equations (SPDEs). For a random field with Matérn covariance, the precision matrix (the inverse of the covariance matrix) corresponds to the finite element stiffness matrix of a potentially fractional PDE involving a second-order elliptic operator. By …
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Calculation of electrical conductivity and electrothermal analysis of multilayered carbon reinforced composites: application to damage detection
… The electrical problem can be expressed by an elliptic PDE, for the case where the material is electrically anisotropic and homogeneous, or non-homogeneous. On the other hand, the transient heat transfer problem involves the case where the material is thermally anisotropic and homogeneous. …
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Hessian Matrix-Free Lagrange-Newton-Krylov-Schur-Schwarz Methods for Elliptic Inverse Problems
… focuses on the solution of inverse problems for elliptic systems. The inverse problem is constructed as a PDE-constrained optimization, where the cost function is the <em>L</em><sup>2</sup> norm of the difference between the measured data and the predicted state variable, and the constraint is an …
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Asymptotic theory for Bayesian nonparametric inference in statistical models arising from partial differential equations
Partial differential equations (PDEs) are primary mathematical tools to model the behaviour of complex real-world systems. PDEs generally include a collection of parameters in their formulation, which are often unknown in applications and need to be estimated from the data. In the present thesis, …
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NEW COMPUTATIONAL METHODS FOR OPTIMAL CONTROL OF PARTIAL DIFFERENTIAL EQUATIONS
… control of partial differential equations (PDEs) has tremendous applications in engineering and science, such as shape optimization, image processing, fluid dynamics, and chemical processes. In this thesis, we develop and analyze several efficient numerical methods for the optimal control …