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Numerical Analysis and Computation Commons™
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- Anisotropic diffusion (1)
- Convergence of Fourier Series (1)
- Deblurring (1)
- Denoising (1)
- Diffusion problems (1)
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- Fast Fourier Transform (1)
- Flow in porous media (1)
- Forward-Backward-Forward Diffusion (1)
- Fourier analysis (1)
- Grid refinement (1)
- Lanczos sigma factor (1)
- Least squares problem (1)
- Nelder-Mead Optimization (1)
- Partial Differential Equations (1)
- Schrodinger Operators (1)
- Sigma approximation (1)
- Signal processing (1)
- Spectral methods (1)
- Stability (1)
- Text Images (1)
- Variable compact multipoint method (1)
- Wave equation (1)
- Publication
Articles 1 - 5 of 5
Full-Text Articles in Numerical Analysis and Computation
Diagonalization Of 1-D Schrodinger Operators With Piecewise Constant Potentials, Sarah Wright
Diagonalization Of 1-D Schrodinger Operators With Piecewise Constant Potentials, Sarah Wright
Master's Theses
In today's world our lives are very layered. My research is meant to adapt current inefficient numerical methods to more accurately model the complex situations we encounter. This project focuses on a specific equation that is used to model sound speed in the ocean. As depth increases, the sound speed changes. This means the variable related to the sound speed is not constant. We will modify this variable so that it is piecewise constant. The specific operator in this equation also makes current time-stepping methods not practical. The method used here will apply an eigenfunction expansion technique used in previous …
Stability Analysis Of Krylov Subspace Spectral Methods For The 1-D Wave Equation In Inhomogeneous Media, Bailey Rester
Stability Analysis Of Krylov Subspace Spectral Methods For The 1-D Wave Equation In Inhomogeneous Media, Bailey Rester
Master's Theses
Krylov subspace spectral (KSS) methods are high-order accurate, explicit time-stepping methods for partial differential equations (PDEs) that also possess the stability characteristic of implicit methods. Unlike other time-stepping approaches, KSS methods compute each Fourier coefficient of the solution from an individualized approximation of the solution operator of the PDE. As a result, KSS methods scale effectively to higher spatial resolution. This thesis will present a stability analysis of a first-order KSS method applied to the wave equation in inhomogeneous media.
An Adaptive Approach To Gibbs’ Phenomenon, Jannatul Ferdous Chhoa
An Adaptive Approach To Gibbs’ Phenomenon, Jannatul Ferdous Chhoa
Master's Theses
Gibbs’ Phenomenon, an unusual behavior of functions with sharp jumps, is encountered while applying the Fourier Transform on them. The resulting reconstructions have high frequency oscillations near the jumps making the reconstructions far from being accurate. To get rid of the unwanted oscillations, we used the Lanczos sigma factor to adjust the Fourier series and we came across three cases. Out of the three, two of them failed to give us the right reconstructions because either it was removing the oscillations partially but not entirely or it was completely removing them but smoothing out the jumps a little too much. …
Variable Compact Multi-Point Upscaling Schemes For Anisotropic Diffusion Problems In Three-Dimensions, James Quinlan
Variable Compact Multi-Point Upscaling Schemes For Anisotropic Diffusion Problems In Three-Dimensions, James Quinlan
Dissertations
Simulation is a useful tool to mitigate risk and uncertainty in subsurface flow models that contain geometrically complex features and in which the permeability field is highly heterogeneous. However, due to the level of detail in the underlying geocellular description, an upscaling procedure is needed to generate a coarsened model that is computationally feasible to perform simulations. These procedures require additional attention when coefficients in the system exhibit full-tensor anisotropy due to heterogeneity or not aligned with the computational grid. In this thesis, we generalize a multi-point finite volume scheme in several ways and benchmark it against the industry-standard routines. …
Automatic Numerical Methods For Enhancement Of Blurred Text-Images Via Optimization And Nonlinear Diffusion, Aaditya Kharel
Automatic Numerical Methods For Enhancement Of Blurred Text-Images Via Optimization And Nonlinear Diffusion, Aaditya Kharel
Honors Theses
In this paper, we propose an automatic numerical method for solving a nonlinear partialdifferential- equation (PDE) based image-processing model. The Perona-Malik diffusion equation (PME) accounts for both forward and backward diffusion regimes so as to perform simultaneous denoising and deblurring depending on the value of the gradient. One of the limitations of this equation is that a large value of the gradient for backward diffusion can lead to singularity formation or staircasing. Guidotti-Kim-Lambers (GKL) came up with a bound for backward diffusion to prevent staircasing, where the backward diffusion is only limited to a specific range beyond which backward diffusion …