Browsing UMBC Mathematics and Statistics Department by Title
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Fast implementation of mixed RT0 finite elements in MATLAB
We develop a fast implementation of the mixed finite element method for the Darcy’s problem discretized by lowestorder RaviartThomas finite elements using Matlab. The implementation is based on the socalled vectorized ... 
FEM Convergence for PDEs with Point Sources in 2D and 3D
(2015)Numerical theory provides the basis for quantification of the accuracy and reliability of a FEM solution by error estimates on the FEM error vs. the mesh spacing of the FEM mesh. This paper presents techniques needed in ... 
FEM Convergence Studies for 2D and 3D Elliptic PDEs with Smooth and NonSmooth Source Terms in COMSOL 5.1
(2015)Numerical theory provides the basis for quanti cation on the accuracy and reliability of a FEM solution by error estimates on the FEM error vs. the mesh spacing of the FEM mesh. This paper presents techniques needed in ... 
Finite element approximation for timedependent diffusion with measurevalued source
(SpringerVerlag, 20120620)The convergence of finite element methods for elliptic and parabolic partial differential equations is wellestablished if source terms are sufficiently smooth. Noting that finite element computation is easily implemented ... 
Finite Element Convergence for TimeDependent PDEs with a Point Source in COMSOL 4.2
(2011)The FEM theory provides the basis for quantification on the accuracy and reliability of a numerical solution by the a priori error estimates on the FEM error vs. the mesh spacing of the FEM mesh. This paper presents ... 
Finite Element Convergence Studies Using COMSOL 4.0a and LiveLink for MATLAB
(2010)In order to gauge how reasonable a finite element solution to a partial differential equation is on a given mesh, a common strategy is to refine the mesh, compute the solution on the finer mesh, and use the solutions on ... 
Fully Distributed Optimization based CAV Platooning Control under Linear Vehicle Dynamics
This paper develops distributed optimization based, platoon centered CAV car following schemes, motivated by the recent interest in CAV platooning technologies. Various distributed optimization or control schemes have been ... 
A generalized model of flocking with steering
(20210207)We introduce and analyze a model for the dynamics of flocking and steering of a finite number of agents. In this model, each agent's acceleration consists of flocking and steering components. The flocking component is a ... 
A GPU Memory System Comparison for an Elliptic Test Problem
This paper presents GPUbased solutions to the Poisson equation with homogeneous Dirichlet boundary conditions in two spatial dimensions. This problem has wellunderstood behavior, but similar computation to many more ... 
The Graph 500 Benchmark on a MediumSize DistributedMemory Cluster with HighPerformance Interconnect
(20121217)While traditional performance benchmarks for highperformance computers measure the speed of arithmetic operations, memory access time is a more useful performance gauge for many large problems today. The Graph 500 benchmark ... 
Graph 500 Performance on a DistributedMemory Cluster
(2012)Social network and medical informatics analysis are examples of modern computing problems that involve large data sets. These data can be represented using graphs, which are sets of vertices that are connected by edges. ... 
A High‐Dimensional Classification Rule Using Sample Covariance Matrix Equipped With Adjusted Estimated Eigenvalues
(Wiley Online Library, 20210203)High‐dimensional classification have had challenges mainly due to the singularity issue of the sample covariance matrix. In this work, we propose a different approach to get a more reliable sample covariance matrix by ... 
A Hölder type inequality and an interpolation theorem in Euclidean Jordan algebras
(20180914)In a Euclidean Jordan algebra V of rank n which carries the trace inner product, to each element x we associate the eigenvalue vector λ(x) whose components are the eigenvalues of x written in the decreasing order. For any ... 
Hybrid MPI+OpenMP parallelization of image reconstruction in proton beam therapy on multicore and manycore processors
The advantage of proton beam therapy is that the lethal dose of radiation is delivered by a sharp increase toward the end of the beam range, known as the Bragg peak (BP), with no dose delivered beyond. By using these ... 
Identifying Nonlinear Correlations in High Dimensional Data with Application to Protein Molecular Dynamics Simulations
(2013)Complex biomolecules such as proteins can respond to changes in their environment through a process called allostery, which plays an important role in regulating the function of these biomolecules. Allostery occurs when ... 
IDL: A Possible Alternative to Matlab
(2012)Created by Exelis Visual Information Solutions, IDL (Interactive Data Language) is a commercial package used for data analysis. We compared the usability and efficiency of IDL to that of Matlab to determine if IDL is a ... 
Impact of Calcium Store Overload and Electrical Dynamics on Cardiac Myocytes
(2015)The heart's main function of pumping blood to the body is a complicated process separated into two major steps. Initially, the heart is relaxed and blood flows freely into the ventricles and atria from the veins, then the ... 
An Implementation of Binomial Method of Option Pricing using Parallel Computing
The Binomial method of option pricing is based on iterating over discounted option payoffs in a recursive fashion to calculate the present value of an option. Implementing the Binomial method to exploit the resources of a ... 
Improvements to the Deep Learning Classification of Compton Camera Based Prompt Gamma Imaging for Proton Radiotherapy
(202005)Realtime imaging has potential to greatly increase the effectiveness of proton beam therapy for cancer treatment. One promising method of realtime imaging is the use of a Compton camera to detect prompt gamma rays, which ... 
Improving the Computational Effciency of Downscaling GCM data for Use in SWAT
(2014)This project creates software tools to streamline the computational procedures to generate highresolution weather parameters from low resolution Global Climate Models (GCM) to be input into the Soil and Water Assessment ...