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 20 of 22 for “"Solving partial differential equations"”.
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Application of Lie symmetries to Solving Partial Differential Equations associated with the Mathematics of Finance
… confronted with a complicated system of partial differential equations arising from some physical important problem, and the discovery of the explicit solution of the problem can result with very useful information. That is, the explicit solutions of the financial market models can be …
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Opportunities for the deep neural network method of solving partial differential equations in the computational study of biomolecules driven through periodic geometries
… network method, in which the solution to a differential equation is approximated by varying the parameters of a deep neural network trial function. Although this idea has been explored with shallow neural networks since the 1990s, it has experienced a resurgence of interest in recent years …
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Pricing interest rate contingent claims
… derivations make use of regular techniques in solving partial differential equations and the risk-neutral pricing methodology.
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Application of a Numerical Method and Optimal Control Theory to a Partial Differential Equation Model for a Bacterial Infection in a Chronic Wound
… techniques and a numerical method to a system of partial differential equations arising from a problem in wound healing. Optimal control theory is a generalization of calculus of variations, as well as the method of Lagrange Multipliers. Both of these techniques have seen prevalent use in the …
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Layer potential evaluations on distributed memory machines
… of using integral equation methods (IEM) for solving partial differential equations is evaluating layer potentials with singular kernels. Quadrature by Expansion (QBX) is a quadrature method to evaluate such layer potentials accurately for targets near or on the source boundary, by forming …
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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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A numerical method for systems of ordinary differential equations
… and simplicity of a new computational method of solving systems of ordinary differential equations. The central idea of this new method revolves around our ability to generate a numerical approximation of the general solution of systems of linear differential equations. The idea of obtaining a …
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A low order acceleration scheme for solving the neutron transport equation
… (MOC) is a widely used technique for solving partial differential equations, and has been applied to the neutron transport problems for many years. The MOC method requires many transport iterations to solve large heterogeneous LWR reactor problems with high dominance ratio, and …
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A Real Options Valuation of Renewable Energy Projects
… bootstrapping and finite difference methods for solving partial differential equations. It is determined that, as correlation between corn price and gasoline price increases, the value of the ethanol plant decreases. The level of decrease is substantial, and the economic and political …
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A multilevel method for meshless solution of the poisson equation in heat transfer and fluid flow
… attractive alternative to grid based methods for solving partial differential equations in complex geometries. Gaussian, Multiquadratics and inverse Multiquadratics are some of the more popular RBF's, but the require a shape paramter for a stable and accurate solution and also face stagnation …
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Numerical Methods in Deep Learning and Computer Vision
… discovery, and physics-informed techniques for solving partial differential equations in disentangled and equivariant representation learning. We first propose two numerical solvers for the faster computation of matrix square root and its inverse. The proposed algorithms are demonstrated to have …
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Dynamic Modeling and Real-time Simulation of Power Electronics-dominated Power Grids Using Hybrid DDM and EDDM Techniques
… electrical power systems necessitates solving numerous differential algebraic equations. As modern grids grow in size and complexity, traditional sequential simulation methods have become increasingly computationally challenging and time-consuming. This research investigates parallelism …
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Polynomial-Based Methods for Time-Integration
… integration methods that can be derived without solving nonlinear order conditions. In part I, we introduce a time-integration framework for solving systems of first-order ordinary differential equations by using interpolating polynomials. Our approach is to combine ideas from complex analysis …
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High performance simulations of yield stress fluids in a structured adaptive mesh refinement framework with embedded boundaries
… includes state-of-the-art numerical tools for solving partial differential equations with optimal parallel scaling. The ability to rapidly simulate unsteady viscoplastic flow problems in three dimensions is demonstrated by novel numerical experiments in a lid-driven cavity. In order to …
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Time Integration Methods for Large-scale Scientific Simulations
… arise from a method of lines approach to solving partial differential equations, resulting in very large systems of equations that require the use of numerical time integration methods to solve. Many problems of scientific interest exhibit stiff behavior for which implicit methods are …
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The real space finite element Hartree-Fock method and the thermo-mechanical properties of carbon nanotubes
… general numerical technique in mathematics for solving partial differential equations (PDEs) and it has been widely applied in computational mechanics and engineering in general, but it has not been extensively used in science for electronic structure calculations. Currently most electronic …
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Parametric curve and Partial Differential Equation-based parametric surface reconstruction from point clouds
… sur- face reconstruction methods lies in solving partial differential equations, which is why most studies have focused on implicit PDE-based shape reconstruction, despite its computational ex- pense. To address these challenges, we propose a novel method that uses an accurate closed-form …
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Water Quality Control in Distribution Systems: Bayesian Optimization & Physics-Informed Machine Learning
… by means of physics-based models that involve solving complex, nonlinear systems of partial differential equations (PDEs) to simulate the underlying physical processes that govern chlorine transport and decay in the WDS. This dissertation aims to address these key challenges by developing …
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Mathematical Study on the Expressive Power of Machine Learning and Applications in Optimal Filtering Problems
… transferable neural networks (TransNet) for solving partial differential equations (PDEs) by reducing the optimization difficulty through the idea of transfer learning. The construction of transferable neural feature spaces involves re-parameterization of hidden neurons and auxiliary …
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A Detailed Treatment of the Measurement of Transport Coefficients in Transient Grating Experiments
… and the derivation of the phenomenological equations. This part is based on the books by de Groot and Mazur and by Haase and contains also some own results. We have explicitely derived a relation between reversible work and dissipation function, if heat and mass are exchanged reversibly and …
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