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- Mixed finite element method (2)
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Articles 1 - 9 of 9
Full-Text Articles in Physical Sciences and Mathematics
Explicit Level Lowering Of 2-Dimensional Modular Galois Representations, Rodney Keaton
Explicit Level Lowering Of 2-Dimensional Modular Galois Representations, Rodney Keaton
All Theses
Let f be a normalized eigenform of level Npα for some positive integer α and some odd prime p satisfying gcd(p,N)=1. A construction of Deligne, Shimura, et. al., attaches a p-adic continuous two-dimensional Galois representation to f. The Refined Conjecture of Serre states that such a representation should in fact arise from a normalized eigenform of level prime to p.
In this presentation we present a proof of Ribet which allows us to 'strip' these powers of p from the level while still retaining the original Galois representation, i.e., the residual of our new representation arising from level N will …
Quantum Codes From Two-Point Hermitian Codes, Justine Hyde-Volpe
Quantum Codes From Two-Point Hermitian Codes, Justine Hyde-Volpe
All Theses
We explore the background on error-correcting codes, including linear codes and quantum codes from curves. Then we consider the parameters of quantum codes constructed from two-point Hermitian codes.
Numerical Modeling Of Contaminant Transport In Fractured Porous Media Using Mixed Finite Element And Finite Volume Methods, Chen Dong
All Theses
A mathematical model for contaminant species passing through fractured porous media is presented. In the numerical model, we combine two locally conservative methods, i.e. mixed finite element (MFE) and the finite volume methods. Adaptive triangle mesh is used for effective treatment of the fractures. A hybrid MFE method is employed to provide an accurate approximation of velocities field for both the fractures and matrix which are crucial to the convection part of the transport equation. The finite volume method and the standard MFE method are used to approximate the convection and dispersion terms respectively. Numerical examples in different fractured media …
Contaminant Flow And Transport Simulation In Cracked Porous Media Using Locally Conservative Schemes, Pu Song
Contaminant Flow And Transport Simulation In Cracked Porous Media Using Locally Conservative Schemes, Pu Song
All Theses
The purpose of this paper is to analyze some features of contaminant flow passing through cracked porous media, such as the influence of fracture network on the advection and diffusion of contaminant species, the adsorption impact of contaminant wastes on the overall transport flow and so on. In order to precisely describe the whole process, we firstly need to build the mathematical model to simulate this problem numerically. Taking into consideration of the characteristics of contaminant flow, we employ two partial differential equations to formulate the whole problem. One is flow equation, the other is reactive transport equation. The first …
Compressive Sensing, Yue Mao
Compressive Sensing, Yue Mao
All Theses
Compressive sensing is a novel paradigm for acquiring signals and has a wide range of applications. The basic assumption is that one can recover a sparse or compressible signal from far fewer measurements than traditional methods. The difficulty lies in the construction of efficient recovery algorithms. In this thesis, we review two main approaches for solving the sparse recovery problem in compressive sensing: l1-minimization methods and greedy methods. Our contribution is that we look at compressive sensing from a different point of view by connecting it with sparse interpolation. We introduce a new algorithm for compressive sensing called generalized eigenvalues …
Sparse Representation For Detection Of Transients Using A Multi-Resolution Representation Of The Auto-Correlation Of Wavelets, Caroline Sieger
Sparse Representation For Detection Of Transients Using A Multi-Resolution Representation Of The Auto-Correlation Of Wavelets, Caroline Sieger
All Theses
This thesis seeks to detect damped sinusoidal transients, specifically capacitor switching transients, buried in noise and to answer the following questions: 1.) Can the transient s(t;q) be sparsely represented from s&delta(t) = s(t;q) + &epsilon(t) using sparsity methods, where &epsilon(t) is white Gaussian noise? 2.) Does computing the local auto-correlation of the signal around the transient improve detection? 3.) How does the auto-correlation shell representation compare to the wavelet representation? 4.) Which basis is ''best''? 5.) Which method and representation is best? This thesis explores detection schemes based on classical methods and newer sparsity methods. Classical methods considered include reconstruction …
Increased Accuracy And Efficiency In Finite Element Computations Of The Leray-Deconvolution Model Of Turbulence, Abigail Bowers
Increased Accuracy And Efficiency In Finite Element Computations Of The Leray-Deconvolution Model Of Turbulence, Abigail Bowers
All Theses
This thesis develops, analyzes and tests a finite element method for approximating solutions to the Leray–deconvolution regularization of the Navier–Stokes equations. The scheme combines three ideas in order to create an accurate and effective algorithm: the use of an incompressible filter, a linearization that decouples the velocity–pressure system from the filtering and deconvolution operations, and a stabilization that works well with the linearization. A rigorous and complete numerical analysis of the scheme is given, and numerical experiments are presented that show clear advantages of the scheme.
The Steiner Linear Ordering Problem: Application To Resource-Constrained Scheduling Problems, Mariah Magagnotti
The Steiner Linear Ordering Problem: Application To Resource-Constrained Scheduling Problems, Mariah Magagnotti
All Theses
When examined through polyhedral study, the resource-constrained scheduling problems have always dealt with processes which have the same priority. With the Steiner Linear Ordering problem, we can address systems where the elements involved have different levels of priority, either high or low. This allows us greater flexibility in modeling different resource-constrained scheduling problems. In this paper, we address both the linear ordering problem and its application to scheduling problems, and provide a polyhedral study of the associated polytopes.
A Numerical Study Of Subgrid Artificial Viscosity Methods For The Navier-Stokes Equations, Keith Galvin
A Numerical Study Of Subgrid Artificial Viscosity Methods For The Navier-Stokes Equations, Keith Galvin
All Theses
This paper studies two artificial viscosity methods for approximating solutions to the Navier&ndashStokes Equations. Both methods that are introduced add stabilization, then remove it only on a coarse mesh. Both methods can be considered as conforming, mixed methods for 1) velocity and its gradient, and 2) velocity and vorticity. Herein we rigorously study the schemes both analytically and computationally, showing that both methods are unconditionally stable and optimally convergent. Numerical experiments show both methods provide improved results over the unstabilized Navier&ndashStokes Equations.