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 36 for “"Optimal convergence"”.
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Nonconforming Immersed Finite Element Methods for Interface Problems
… analysis, we prove that these IFE spaces have optimal approximation capabilities. We use these IFE spaces to develop partially penalized Galerkin (PPG) IFE schemes whose bilinear forms contain penalty terms over interface edges. Error estimation is carried out for these IFE schemes. We prove …
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ΜΕΘΟΔΟΙ ΠΑΡΕΜΒΟΛΗΣ ΜΕ Ο(Η6) ΣΥΓΚΛΙΣΗ ΓΙΑ ΕΛΛΕΙΠΤΙΚΕΣ ΕΞΙΣΩΣΕΙΣ 2ΗΣ ΚΑΙ 4ΗΣ ΤΑΞΗΣ
IN THIS THESIS WE DEVELOP AND ANALYZE OPTIMAL COLLOCATION METHODS FOR SECOND AND FOURTH ORDER TWO-POINT BOUNDARY VALUE PROBLEMS (LINEAR AND NON LINEAR). THESEDIFFERENTIAL EQUATIONS ARE CONSIDERED TO BE DEFINED IN SPACES R AND R2 AND THEIR SOLUTION SATISFIES SOME BOUNDARY CONDITIONS. THE …
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Semiparametric mixture models
… algorithms have been proposed to achieve the optimal convergence rate for both the global parameters and nonparametric regression functions. We derive the asymptotic property of the proposed estimates and show that both proposed EM-type algorithms preserve the asymptotic ascent property. In …
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A Spacetime Discontinuous Galerkin Finite-Element Method for Elastodynamic Analysis
… results. The second study investigates the convergence properties of the numerical model. Numerical results report that the method delivers optimal convergence rate. The third study involves a crack-tip wave scattering problem, in which a step loading is applied to a solid medium of finite …
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Design, Analysis, and Application of Immersed Finite Element Methods
… penalized IFE (PPIFE) scheme and prove its optimal convergence rates. Secondly, we discuss the limitations of the current approaches of IFE methods when we try to extend them to higher degree IFE methods. Then we develop a new framework to construct and analyze arbitrary p-th degree IFE …
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Non-Intrusive Extension of a Generalized Finite Element Method for Multiscale Problems to the Abaqus Analysis Platform
… CAE/FEA software packages in order to obtain optimal convergence for challenging multiscale problems.
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Immersed Finite Elements for a Second Order Elliptic Operator and Their Applications
… new estimation further enables us to show the optimal convergence in the $L^2$ norm which could not be done by the analysis presented in [111]. Then we consider applications of IFEs developed for the second order elliptic operator to wave propagation and diffusion interface problems. The first …
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Bilinear Immersed Finite Elements For Interface Problems
… based on the bilinear IFE spaces have the same optimal convergence rates as those based on the standard bilinear finite element for solutions with certain smoothness. For the symmetric selective immersed discontinuous Galerkin method based on bilinear IFE, we have established its optimal …
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Wavelet regression with long memory infinite moving average errors
… average errors, and investigate the rates of convergence of estimators based on thresholding of empirical wavelet coefficients. We show that these estimators achieve nearly optimal minimax convergence rates within a logarithmic term over a large class of non-smooth functions that involve many …
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Essays on Algorithmic Learning and Uncertainty Quantification
… called the star algorithm can recover near-optimal convergence rates for non-parametric logistic regression in non-convex models. The second essay, titled “Kernel Ridge Regression Inference,” introduces a new technique for deriving sharp, non-asymptotic, uniform Gaussian approximation for …
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A fast enriched FEM for Poisson equations involving interfaces
… enriched basis functions to make sure that the optimal convergence rates are obtained. Here, the FFT is applied in the fast Poisson solver to significantly accelerate the computational processes for solving the global matrix system. With reasonably small interfaces, the operational cost is …
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Covolume-Upwind Finite Volume Approximations For Linear Elliptic Partial Differential Equations
… out to numerically demonstrate stability and optimal convergence of the proposed methods.</p>
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Improved conditioning and accuracy of a two-scale generalized finite element method for fracture mechanics
… presented along with numerical verification of convergence properties predicted by the estimate. The analysis shows optimal convergence of the method on problems with strong singularities and the method can deliver the same accuracy as direct numerical simulations (DNS) while using much fewer …
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Sampling Controlled Stochastic Recursions: Applications to Simulation Optimization and Stochastic Root Finding
… sequence of algorithmic parameters to guarantee convergence. The theory for choosing such parameters is now well-established, but most such theory focuses on asymptotic performance. Automatically choosing parameters to ensure good finite-time performance has remained vexingly elusive, as …
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A consistent segment procedure for solution of 2D contact problems with large displacements
… the patch test is a fundamental requirement for optimal convergence of the finite element solution. The algorithm is a Lagrange-multiplier based one, with the contact tractions as the additional variables to be solved for. Interpolation orders for which the resulting mixed formulation remains …
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Making Sense of Training Large AI Models
… we also prove that Adam achieves the optimal convergence rate in various non-convex optimization settings, both smooth and non-smooth settings. The third part of this thesis focuses on the unstable convergence phenomenon in training large models. We identify its main characteristics …
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On triangular finite elements for general shell structures
… Indeed, there does not exist yet a "uniformly optimal" triangular shell element. The work in this thesis focuses on the development of continuum mechanics based triangular shell elements (of low and high order) which overcome the known disadvantages and show uniform optimal convergence. As the …
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A Discontinuous Galerkin Method for Higher-Order Differential Equations Applied to the Wave Equation
… where the finite element solution exhibits an optimal convergence rate in the L2- norm. We further show that the q-degree discontinuous solution of a differential equation of order m and its first (m-1)-derivatives are strongly superconvergent at the end of each step. We also establish that the …
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Consensus-type stochastic approximation algorithms
… this dissertation demonstrates that asymptotic optimality can be achieved in convergence rates of stochastic approximation algorithms for consensus control with structural constraints. The algorithm involves two stages. The first stage is a coarse approximation obtained using a sequence of large …
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Immersed and Discontinuous Finite Element Methods
In this dissertation we prove the superconvergence of the minimal-dissipation local discontinuous Galerkin method for elliptic problems and construct optimal immersed finite element approximations and discontinuous immersed finite element methods for the Stokes interface problem. In the first part …
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