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Some of the material in is restricted to members of the community. By logging in, you may be able to gain additional access to certain collections or items. If you have questions about access or logging in, please use the form on the Contact Page.
Many numerical methods based on Radial Basis Functions (RBFs) are gaining popularity in the geosciences due to their competitive accuracy, functionality on unstructured meshes, and natural extension into higher dimensions. One method in...
Spherical centroidal Voronoi tessellations (SCVT) are used in many applications in a variety of fields, one being climate modeling. They are a natural choice for spatial discretizations on the surface of the Earth. New modeling...
The objective of this work is the development of novel, efficient and reliable sparse grid stochastic collocation methods for solving linear and nonlinear partial differential equations (PDEs) with random coefficients and forcing terms ...
Estimating groundwater nitrate fate and transport is an important task in water resources and environmental management because excess nitrate loads may have negative impacts on human and environmental health. This work discusses the...
Analysis of Two Partial Differential Equation Models in Fluid Mechanics: Nonlinear Spectral Eddy-Viscosity Model of Turbulence and Infinite-Prandtl-Number Model of Mantle Convection
This thesis presents two problems in the mathematical and numerical analysis of partial differential equations modeling fluids. The first is related to modeling of turbulence phenomena. One of the objectives in simulating turbulence is...
The work in this thesis is motivated by the application of spray combustion. If one develops algorithms to simulate spray generation, for example the primary break-up of a liquid jet in a gas cross-flow, then a body-fitted or Lagrangian...
Mesh generation in regions in Euclidean space is a central task in computational science, especially for commonly used numerical methods for the solution of partial differential equations (PDEs), e.g., finite element and finite volume...
This thesis explores possible improvements in the construction of Delaunay Triangulations on the Sphere by designing and implementing a parallel alternative to the software package STRIPACK. First, it gives an introduction to Delaunay...
This dissertation includes the application of analysis-of-variance (ANOVA) expansions to analyze solutions of parameter dependent partial differential equations and the analysis and finite element approximations of the Stokes equations...
This work focuses on developing and analyzing novel, efficient sparse-grid algorithms for solving several types of stochastic ordinary/partial differential equations and corresponding inverse problem, such as parameter identification....
This dissertation focuses on the non local continuum peridynamics model for the mechanics of materials, related constitutive models, its connections to molecular dynamics and classical elasticity, and its multiscale and multimodel...
In this dissertation, the recently developed peridynamic nonlocal continuum model for solid mechanics is extensively studied, specifically, the numerical methods for the deterministic and stochastic steady-state peridynamics models. In...
We are exploring the effect of using various vertical mixing closures on resolving the physical process known as overflow. This is when cold dense water overflows from a basin in the ocean. This process is responsible for the majority of...
In 4D-Var data assimilation for geophysical models, the goal is to reduce the lack of fit between model and observations (strong constraint approach assuming perfect model). In the last two decades four dimensional variational technique...
In this thesis, we tackle the fundamental problem of how to effectively and reliably calculate sparse solutions to underdetermined systems of equations. This class of problems is found in applied mathematics, electrical engineering, ...
Centroidal Voronoi tessellations (CVTs) are special Voronoi tessellations whose generators are also the centers of mass (centroids) of the Voronoi regions with respect to a given density function. CVT-based algorithms have been proved...
Metadynamics is a popular tool to explore free energy landscapes and it has been use to elucidate various chemical or biochemical processes. The height of updating Gaussian function is very important for proper free energy convergence to...
Some of the material in is restricted to members of the community. By logging in, you may be able to gain additional access to certain collections or items. If you have questions about access or logging in, please use the form on the Contact Page.
