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Skip to Search Results- 6Han, Bin (Mathematical and Statistical Sciences)
- 3Minev, Peter (Mathematical and Statistical Sciences)
- 2Wong, Yau Shu (Mathematical and Statistical Sciences)
- 1Belhamadia, Youssef (Department of Mathematical and Statistical Sciences and Department of Biomedical Engineering)
- 1Finlay, Warren (Mechanical Engineering)
- 1Wong, Yau S (Mathematical and Statistical Sciences)
- 1Alveoli
- 1Biorthogonal and orthogonal multiwavelets
- 1Body force
- 1Boundary wavelets
- 1Bounded interval
- 1Compact finite difference method
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Fall 2017
One main goal of this thesis is to bring forth a systematic and simple construction of a multiwavelet basis on a bounded interval. The construction that we present possesses orthogonality in the derivatives of the multiwavelet basis among all scale levels. Since we are mainly interested in Riesz...
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Fall 2014
This thesis presents recent developments in direct numerical simulations of fluid-structure interaction occurring in biological systems, with particular interest in the modeling of particle deposition within the human respiratory system. Two numerical techniques are proposed. The first one is...
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Fall 2015
This thesis concentrates on the construction of directional tensor product complex tight framelets. It uses a complex tight framelet filter bank in one dimension and the tensor product of the one-dimensional filter bank to obtain high-dimensional filter bank. It has a number of advantages over...
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Fall 2022
Interface problems arise in many applications such as modeling of underground waste disposal, oil reservoirs, composite materials, and many others. The coefficient $a$, the source term $f$, the solution $u$ and the flux $a\nabla u\cdot \vec{n}$ are possibly discontinuous across the interface...
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Fall 2022
The Helmholtz equation is a fundamental wave propagation model in the time-harmonic setting, which appears in many applications such as electromagnetics, geophysics, and ocean acoustics. It is challenging and computationally expensive to solve due to (1) its highly oscillating solution and (2)...
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Spring 2021
Generalizing wavelets by adding desired redundancy and flexibility, framelets (a.k.a. wavelet frames) are of interest and importance in many applications such as image processing and numerical algorithms. Several key properties of framelets are high vanishing moments for sparse multi-scale...
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The Strong Restricted Isometry Property of Sub-Gaussian Matrices and the Erasure Robustness Property of Gaussian Random Frames
DownloadSpring 2016
In this thesis we will study the robustness property of sub-gaussian random matrices. We first show that the nearly isometry property will still hold with high probability if we erase a certain portion of rows from a sub-gaussian matrix, and we will estimate the erasure ratio with a given small...