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Applied Mathematics Theses and Dissertations

Theses and Dissertations for the Applied Mathematics department.

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Items (1-14) out of 14 results

A Level-Sets-Based Wavefront Propagation Method for Underwater Acoustics

Description:
Computer models for underwater sound propagation often rely on ray tracing to obtain solutions to the high frequency wave equation. While adequate for large scale …
Year:
2012
Contributor:
Martinelli, Sheri L (creator)
Hesthaven, Jan (Director)
Shu, Chi-Wang (Reader)
Siegmann, William (Reader)
Brown University. Applied Mathematics (sponsor)
Genre:
theses
Subject:
high frequency acoustics
geometric optics
WENO
scientific computing
Level set methods
Geometrical optics
Language:
English
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

A Spectral Element Method for Fluid-Structure Interaction : New Algorithm and Applications to Intracranial Aneurysms

Description:
The first part of the thesis presents the surface respresentation of blood vessel walls extracted from medical images, sensitivity to the inlet/outlet boundary conditions, and …
Year:
2010
Contributor:
Baek, Hyoungsu (creator)
Karniadakis, George (Director)
Shu, Chi-Wang (Reader)
Richardson, Peter (Reader)
Bittencourt, Marco (Reader)
Brown University. Applied Mathematics (sponsor)
Genre:
theses
Subject:
spectral method
stability analysis
flow instability
Numerical analysis
Fluid-structure interaction
Stability--Analysis
Aneurysms
Language:
English
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

An O(p^(d+1)) Complexity p-version FEM for Nonlinear Diffusion and Wave Equation in R^d

Description:
The solutions to nonlinear wave equations and diffusion equations often exhibit complicated behavior but the solution is nevertheless quite smooth, which makes high order methods …
Year:
2025
Contributor:
Wang, Mingyu (creator)
Ainsworth, Mark (Advisor)
Shu, Chi-Wang (Reader)
Kirby, Robert (Reader)
Brown University. Department of Applied Mathematics (sponsor)
Genre:
theses
Subject:
Scientific Computation
High performance computing
Finite Element Method (FEM)
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

Analysis and Implementation of Some Stabilized Finite Element Methods Applied to Fluid Mechanics

Description:
In this dissertation we propose, analyze and computationally implement finite element models to two different two-dimensional saddle point systems of partial differential equations with boundary …
Year:
2022
Contributor:
Cáceres-Valenzuela, Ernesto David (creator)
Guzmán, Johnny (Advisor)
Shu, Chi-Wang (Reader)
Barrenechea, Gabriel (Reader)
Brown University. Department of Applied Mathematics (sponsor)
Genre:
theses
Subject:
Finite element method
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

Applications of FEM with Macro-Elements: Discrete Elasticity Sequences and Convergence of Lagrange Elements for a Maxwell Eigenvalue Problem

Description:
In this thesis, we investigate two applications of finite element methods that employ macro-elements: discrete elasticity sequences and convergence of Lagrange elements for a Maxwell …
Year:
2023
Contributor:
Gong, Sining (creator)
Guzmán, Johnny (Advisor)
Shu, Chi-Wang (Reader)
Neilan, Michael (Reader)
Brown University. Department of Applied Mathematics (sponsor)
Genre:
theses
Subject:
Finite element method
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

Compatible high-order meshless schemes for viscous flows through l2 optimization

Description:
Meshless methods provide an ideal framework for scalably simulating Lagrangian hydrodynamics in domains undergoing large deformation. For these schemes, interfaces can easily be treated without …
Year:
2015
Contributor:
Trask, Nathaniel A (creator)
Maxey, Martin (Director)
Karniadakis, George (Reader)
Shu, Chi-Wang (Reader)
Brown University. Applied Mathematics (sponsor)
Genre:
theses
Subject:
compatible discretization
numerical pde
meshless method
mimetic method
Meshfree methods (Numerical analysis)
Graph theory
Computational fluid dynamics
Language:
English
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

Efficient Algorithms for High-Dimensional Hamilton-Jacobi Partial Differential Equations and Optimal Control Problems

Description:
Hamilton-Jacobi partial differential equations (HJ PDEs) have deep connections to a wide range of scientific disciplines including optimal control, differential games, imaging sciences, and machine …
Year:
2023
Contributor:
Chen, Paula (creator)
Darbon, Jerome (Advisor)
Shu, Chi-Wang (Reader)
Hewer, Gary (Reader)
Brown University. Department of Applied Mathematics (sponsor)
Genre:
theses
Subject:
Machine Learning
Field programmable gate arrays
Regression analysis
optimal control
Hamilton-Jacobi equations
Riccati equation
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

Exact Smooth Piecewise Polynomial Sequences on Powell-Sabin and Worsey-Farin Splits

Description:
The problem of forming exact sequences of finite element spaces that discretize Hilbert complexes is central to the finite element exterior calculus. This framework offers …
Year:
2020
Contributor:
Lischke, Anna (creator)
Guzman, Johnny (Advisor)
Neilan, Michael (Reader)
Shu, Chi-Wang (Reader)
Brown University. Department of Applied Mathematics (sponsor)
Genre:
theses
Subject:
Scientific Computation
Numerical analysis
Finite element method
Algebra, Homological
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

High-Performance High-Order Simulation of Wave and Plasma Phenomena

Description:
This thesis presents results aiming to enhance and broaden the applicability of the discontinuous Galerkin (''DG'') method in a variety of ways. DG was chosen …
Year:
2010
Contributor:
Kloeckner, Andreas P (creator)
Hesthaven, Jan (Director)
Guzmán, Johnny (Reader)
Shu, Chi-Wang (Reader)
Brown University. Applied Mathematics (sponsor)
Genre:
theses
Subject:
Discontinuous Galerkin
DG
Parallel Computing
GPU
Shock Capturing
Artificial viscosity
Particle-in-Cell
Multi-Rate ODE solver
Language:
English
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

Novel optimization algorithms for evaluating solution to certain high dimension (multi-time) Hamilton-Jacobi PDEs arising from optimal control

Description:
In this thesis, we study optimization algorithms for evaluating solutions to certain high dimension (multi-time) Hamilton-Jacobi Partial Differential equations arising from optimal control. There are …
Year:
2022
Contributor:
Kim, TaeWoo (creator)
Darbon, Jerome (Advisor)
Shu, Chi-Wang (Reader)
Guzman, Johnny (Reader)
Brown University. Department of Applied Mathematics (sponsor)
Genre:
theses
Subject:
Convex Optimization
optimal control
Hamilton-Jacobi equations
primal dual
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

Overcoming the curse of dimensionality for solving high-dimensional Hamilton-Jacobi partial differential equations using neural networks and optimization algorithms

Description:
Hamilton-Jacobi PDEs and optimal control problems are widely used in many practical problems in control engineering, physics, financial mathematics, and machine learning. For instance, controlling …
Year:
2022
Contributor:
Meng, Tingwei (creator)
Darbon, Jerome (Advisor)
Karniadakis, George (Reader)
Shu, Chi-Wang (Reader)
Brown University. Department of Applied Mathematics (sponsor)
Genre:
theses
Subject:
Optimizations
Neural networks (Computer science)
optimal control
Hamilton-Jacobi equations
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

Preconditioning the p-FEM Mass Matrix: Theory, Implementation, and Applications

Description:
The finite element method (FEM) is an extremely successful approach to numerically approximating solutions to partial differential equations arising from many real-world scenarios. While the …
Year:
2020
Contributor:
Jiang, Shuai (creator)
Ainsworth, Mark (Advisor)
Shu, Chi-Wang (Reader)
Sarkis, Marcus (Reader)
Brown University. Department of Applied Mathematics (sponsor)
Genre:
theses
Subject:
preconditioners
Finite element method
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

Recent Advances in Splitting Methods Based on Robin-Robin Coupling Conditions

Description:
In this thesis we develop a loosely coupled splitting method for coupled problems called the Robin-Robin splitting method. As the name suggests, this method is …
Year:
2022
Contributor:
Durst, Rebecca Frances (creator)
Guzman, Johnny (Advisor)
Shu, Chi-Wang (Reader)
Burman, Erik (Reader)
Brown University. Department of Applied Mathematics (sponsor)
Genre:
theses
Subject:
Numerical analysis
Fluid-structure interaction--Mathematical models
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

Reduced basis methods and their applications

Description:
This thesis presents several model reduction techniques that achieve a comparable accuracy with much less computational cost compared to that of high fidelity numerical simulation. …
Year:
2013
Contributor:
Zhu, Xueyu (creator)
Hesthaven, Jan (Director)
Shu, Chi-Wang (Reader)
Guzman, Johnny (Reader)
Brown University. Applied Mathematics (sponsor)
Genre:
theses
Subject:
reduced basis methods; model reduction
Language:
English
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

Items (1-14) out of 14 results