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Items (61-80) out of 187 results

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

Existence and Stability of Spatially Localized Planar Patterns

Description:
Spatially localized structures, in which a spatially oscillatory pattern on a finite spatial range connects to a trivial homogeneous solution outside this range, have been …
Year:
2015
Contributor:
Makrides, Elizabeth (creator)
Sandstede, Bjorn (Director)
Beck, Margaret (Reader)
Menon, Govind (Reader)
Brown University. Applied Mathematics (sponsor)
Genre:
theses
Subject:
dynamical systems
pattern formation
PDEs
spatial dynamics
Evans function
Dynamics
Pattern formation (Physical sciences)
Language:
English
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

Finite Element Methods for Interface Problems Using Unfitted Meshes: Design and Analysis

Description:
This dissertation aims to study finite element methods for two-dimensional stationary second order interface model problems on homogeneous and heterogeneous media, under discretizations non-fitted with …
Year:
2016
Contributor:
Sanchez, Manuel A (creator)
Guzman, Johnny (Director)
Ainsworth, Mark (Reader)
Sarkis, Marcus (Reader)
Brown University. Applied Mathematics (sponsor)
Genre:
theses
Subject:
interface problems
Finite element method
Language:
English
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

From Kinetic Theory to Fluid Mechanics: Viscous Surface Wave and Hydrodynamic Limit

Description:
In this dissertation, we mainly discuss two topics of partial differential equations in fluid dynamics and kinetic theory: viscous surface wave and diffusive limit. With …
Year:
2015
Contributor:
Wu, Lei (creator)
Guo, Yan (Director)
Shu, Chi-Wang (Director)
Dong, Hongjie (Reader)
Brown University. Applied Mathematics (sponsor)
Genre:
theses
Subject:
free surface
Milne problem
geometric correction
Interpolation
Language:
English
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

Galerkin neural networks for the approximation of partial differential equations with error control

Description:
In the past decade, deep neural networks have seen a dramatic rise in popularity for a wide variety of tasks from computer vision and speech …
Year:
2023
Contributor:
Dong, Justin (creator)
Ainsworth, Mark (Advisor)
Keith, Brendan (Reader)
Stinis, Panagiotis (Reader)
Brown University. Department of Applied Mathematics (sponsor)
Genre:
theses
Subject:
Neural Networks
Differential equations, Partial--Numerical solutions
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

Generative Adversarial Networks for Physics-Informed Learning

Description:
Motivated by the ubiquitous demand of leveraging both data and partial knowledge of physical laws for stochastic modeling and uncertainty quantification, in the dissertation, a …
Year:
2021
Contributor:
Yang, Liu (creator)
Karniadakis, George (Advisor)
Perdikaris, Paris (Reader)
Darbon, Jerome (Reader)
Brown University. Department of Applied Mathematics (sponsor)
Genre:
theses
Subject:
Machine Learning
Data-Driven Scientific Computing
Uncertainty Quantification
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

Geometric, Combinatorial, and Experimental Perspectives on the k-Max-Cut Problem

Description:
The k-max-cut problem is a combinatorial question of great importance in network science and data science. Given a network, the problem seeks a way to …
Year:
2025
Contributor:
Chambers, Teressa (creator)
Klivans, Caroline (Advisor)
Chan, Melody (Reader)
Paul, Alice (Reader)
Brown University. Department of Applied Mathematics (sponsor)
Genre:
theses
Subject:
Combinatorics
Combinatorial geometry
Combinatorial optimization
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

Geometry and Mechanics of Self-Assembled Colloidal Membranes

Description:
Colloidal membranes are an example of a novel bioinspired soft material with rich properties that stem from the interplay of geometry and molecular order. A …
Year:
2018
Contributor:
Jia, Leroy (creator)
Powers, Thomas (Advisor)
Pelcovits, Robert (Advisor)
Matzavinos, Anastasios (Reader)
Brown University. Department of Applied Mathematics (sponsor)
Genre:
theses
Subject:
Soft Matter
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

Grow-Up Solutions and Heteroclinics to Infinity for Scalar Parabolic PDEs

Description:
In recent years, there has been a great deal of interest surrounding the study of the asymptotics and global attractor structure for scalar parabolic PDEs …
Year:
2009
Contributor:
Ben-Gal, Nitsan (creator)
Fieldler, Bernold (director)
Dafermos, Constantine (reader)
Sandstede, Bjorn (reader)
Brown University. Applied Mathematics (sponsor)
Genre:
theses
Subject:
grow-up
global attractor
semilinear parabolic PDE
asymptotic behavior
connecting orbits
inertial manifold
Language:
English
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

High Order 2D Finite Element Methods with Extra Smoothness

Description:
Finite element methods (FEMs) are used to discretize partial differential equations in a wide array of applications, including fluid flow, solid mechanics, electromagnetism, optimal control, …
Year:
2022
Contributor:
Parker, Charles William (creator)
Ainsworth, Mark (Advisor)
Süli, Endre (Reader)
Karniadakis, George (Reader)
Brown University. Department of Applied Mathematics (sponsor)
Genre:
theses
Subject:
Numerical analysis
preconditioners
Finite element method
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

High Order Numerical Methods for Hyperbolic Equations: Bound-preserving and Riemann Invariant Based System Solvers

Description:
This dissertation consists of three topics on bound-preserving discontinuous Galerkin (DG) methods for time-dependent and stationary hyperbolic equations, and efficient finite difference weighted essentially non-oscillatory …
Year:
2023
Contributor:
Xu, Ziyao (creator)
Shu, Chi-Wang (Advisor)
Ainsworth, Mark (Reader)
Guzmán, Johnny (Reader)
Brown University. Department of Applied Mathematics (sponsor)
Genre:
theses
Subject:
Conservation laws (Mathematics)--Numerical solutions
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

High order numerical methods for hyperbolic equations: superconvergence, and applications to δ-singularities and cosmology

Description:
Part I introduces the discontinuous Galerkin (DG) method for solving hyperbolic equations. The introduction and the DG scheme will be given in the first two …
Year:
2013
Contributor:
Yang, Yang (creator)
Shu, Chi-Wang (Director)
Hesthaven, Jan (Reader)
Guzman, Johnny (Reader)
Brown University. Applied Mathematics (sponsor)
Genre:
theses
Subject:
Discontinuous Galerkin method
superconvergence
δ-singularities
WENO scheme
Cosmology
Language:
English
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

High Order Numerical Methods: Entropy Stability and Deterministic Solvers of Stochastic PDEs

Description:
This thesis consists of two diverse topics on high order numerical methods for time-dependent partial differential equations (PDEs). In the first part, we develop a …
Year:
2019
Contributor:
Chen, Tianheng (creator)
Shu, Chi-Wang (Advisor)
Rozovsky, Boris (Reader)
Guzmán, Johnny (Reader)
Brown University. Department of Applied Mathematics (sponsor)
Genre:
theses
Subject:
Discontinuous Galerkin Methods
Conservation laws (Mathematics)--Numerical solutions
Polynomial chaos
Stochastic calculus
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

High Order WENO Scheme for Computational Cosmology

Description:
This dissertation focuses on the analysis and computation of a certain high order accurate numerical scheme which is used to solve problems in computational Cosmology. …
Year:
2010
Contributor:
Roy, Ishani (creator)
Shu, Chi-Wang (Director)
Guzmán, Johnny (Reader)
Hesthaven, Jan (Reader)
Brown University. Applied Mathematics (sponsor)
Genre:
theses
Subject:
Higher order schemes
Scientific computing
Computational Cosmology
Numerical analysis
Language:
English
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

High-Dimensional Response-Excitation PDF Methods for Uncertainty Quantification and Stochastic Modeling

Description:
The probability density approach based on the response-excitation theory is developed for stochastic simulations of non-Markovian systems. This approach provides the complete probabilistic configuration of …
Year:
2015
Contributor:
Cho, Heyrim (creator)
Karniadakis, George (Director)
Rozovsky, Boris (Reader)
Venturi, Daniele (Reader)
Sapsis, Themistoklis (Reader)
Brown University. Applied Mathematics (sponsor)
Genre:
theses
Subject:
Uncertainty quantification
Numerical PDE
Language:
English
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

High-order Accurate Methods for solving Maxwell's equations and their applications

Description:
This thesis contains two topics on high-order accurate methods for solving Maxwell's equations. The first topic is the application of high-order accurate methods to the …
Year:
2008
Contributor:
Chun, Sehun (creator)
Hesthaven, Jan (director)
Gottlieb, David (reader)
Shu, Chi-Wang (reader)
Brown University. Applied Mathematics (sponsor)
Genre:
theses
Subject:
Discontinuous Galerkin method
Maxwell's equations
The frozen mode
Thin layer approximation
PDE constraint optimization
Language:
English
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

Homoclinic Snaking of Spatiotemporal Patterns in Reaction Diffusion Systems

Description:
Abstract of Homoclinic Snaking of Spatiotemporal Patterns in Reaction Diffusion Equations, by Timothy V Roberts, Ph.D., Brown University, May 2024. Spiral and target waves are …
Year:
2024
Contributor:
Roberts, Timothy Victor (creator)
Sandstede, Bjorn (Advisor)
Beck, Margaret (Reader)
Menon, Govind (Reader)
Brown University. Department of Applied Mathematics (sponsor)
Genre:
theses
Subject:
Differential equations, Partial
Applied mathematics
Pattern formation (Biology)
dynamical systems
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

Identifying Diabetic Kidney Disease Risk Factors in the U.S. Population with Type 2 Diabetes Mellitus

Description:
Diabetes is the leading cause of chronic kidney disease and kidney failure worldwide, causing 44 percent of new cases of kidney failure each year. Although …
Year:
2019
Contributor:
Webb, Katherine (creator)
Aubert, Ronald (thesis advisor)
Sandstede, Bjorn (reader)
Brown University. Applied Mathematics (sponsor)
Genre:
theses
Subject:
Applied mathematics
Biology
Diabetes
Diabetic nephropathies
Language:
English
Collection:
Applied Mathematics
Theses and Dissertations
Available to Brown-affiliated users only
Full Record

Image Compression and Data Clustering: New Takes on Some Old Problems

Description:
We explore two topics in this thesis: (1) entropy rate on images, and (2) robust generalized clustering method. On the first topic, we examine the …
Year:
2017
Contributor:
Wang, Wei-Ying (creator)
Geman, Stuart (Advisor)
Harrison, Matthew (Reader)
Bienenstock, Elie (Reader)
Brown University. Department of Applied Mathematics (sponsor)
Genre:
theses
Subject:
Image compression
unsupervised clustering
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

Items (61-80) out of 187 results