Browsing UMBC Mathematics and Statistics Department by Issue Date
Now showing items 2140 of 422

Variational Problems in Weighted Sobolev Spaces with Applications to Computational Fluid Dynamics
(20080819)We study variational problems in weighted Sobolev spaces on bounded domains with angular points. The specific forms of these variational formulations are motivated by, and applied to, a finite element scheme for the ... 
Multispace and multilevel BDDC
(Springer, 20080925)BDDC method is the most advanced method from the Balancing family of iterative substructuring methods for the solution of large systems of linear algebraic equations arising from discretization of elliptic boundary value ... 
Geometric optimization problems with applications to ellipsoidal approximations and quasiNewton methods
(20081009)Our goal in this dissertation is to study some optimization problems with special structure and exploit this structure to obtain additional information that will be useful in the development of numerical methods. In ... 
Partial Differential Equation Constrained Optimization and its Applications to Parameter Estimation in Models of Nerve Dendrites
(20081012)One important application of the parameter identification method in neuroscience is to determine how voltagedependent ion channels are spatially distributed through measurements of voltage along the dendrites. While in ... 
LongTime Simulations on High Resolution Meshes to Model Calcium Waves in a Heart Cell
(Society for Industrial and Applied Mathematics, 20081013)A model for the flow of calcium on the scale of one heart cell is given by a system of timedependent reactiondiffusion equations coupled by nonlinear reaction terms. Calcium ions enter into the cell at release units ... 
Use of Operator Upscaling for Seismic Inversion: Computationally Feasible Forward and Adjoint Calculations
(20081028)To solve seismic inverse problems via the adjoint state method, we must be able to repeatedly solve both the wave equation and its adjoint efficiently. Operator upscaling applied to the wave equation imparts fine scale ... 
Efficient Computation for a ReactionDiffusion System with a Fast Reaction with Continuous and Discontinuous Initial Data Using COMSOL Multiphysics
(2009)In a chemical reactiondiffusion system with three species, the interaction between diffusion and a fast reaction between two species creates a transient, sharp, internal interface. Besides the three species model, we use ... 
Solving a TwoDimensional Elliptic Model Problem with the Conjugate Gradient Method Using MatrixFree SSOR Preconditioning in Matlab
(2009)The existing Preconditioned Conjugate Gradient method in Matlab can be optimized in terms of wall clock time and, more importantly, required storage space. The developed optimized algorithm was tested repeatedly on a two ... 
Efficient Computation for a ReactionDiffusion System with a Fast Reaction in Two Spatial Dimensions Using COMSOL Multiphysics
(2009)We study a reactiondiffusion system of three chemical species, where two chemicals react with a much faster rate than the other reaction in the model. We are interested in the asymptotic limit as the rate becomes in finite. ... 
Performance Comparison between Blocking and NonBlocking Communications for a ThreeDimensional Poisson Problem
(2009)The system of linear equations obtained by finite difference discretization of the threedimensional Poisson problem is solved by a matrixfree parallel implementation of the Jacobi method. After checking the convergence ... 
LongTime Simulation of Calcium Waves in a Heart Cell to Study the Effects of Calcium Release Flux Density and of Coefficients in the Pump and Leak Mechanisms on SelfOrganizing Wave Behavior
(2009)Spontaneous calcium sparks can lead to propagation of a selfinitiated calcium wave under certain conditions in a heart cell. A model for diffusion waves of calcium ions in a heart cell is given by a system of coupled, ... 
Parallel Performance Studies for a Maximum Likelihood Estimation Problem Using TAO
(2009)In this report, we present an application of parallel computing to an estimation procedure in statistics. The method of maximum likelihood estimation (MLE) is based on the ability to perform maximizations of probability ... 
Performance Studies with COMSOL Multiphysics via Scripting and Batch Processing
(2009)COMSOL Multiphysics is an extremely powerful and versatile finite element package for the solution of partial differential equations. While the graphical user interface (GUI) offers a friendly environment for solving small ... 
Performance Studies for Multithreading in Matlab with Usage Instructions on hpc
(2009)This report explores the use of multiple computational cores by multithreading in the software package Matlab on a compute node with two dualcore AMD Opteron processors. After testing the builtin functions of Matlab for ... 
Statistical Analysis based on Physiologicallybased Pharmacokinetic Models
(20090101)Physiologicallybased pharmacokinetic (PBPK) modeling has reached considerable sophistication in its application in the pharmacological and environmental health areas. Yet, mature methodologies for making statistical ... 
Homogenization of Mixed Horizontal LCPs and Applications
(20090101)In optimization, a homogeneous model is an artificial transformation of a given problem. The transformation is done such that the homogeneous problem has always a solution even if the original problem does not. Moreover, ... 
Infeasible interior point methods for sufficient linear complementarity problems
(20090101)In the first part of the thesis we focus on algorithms acting in the small neighborhood of the central path. We present a new first order correctorpredictor method for solving sufficient linear complementarity problems ... 
The Optimal Relaxation Parameter for the SOR Method Applied to the Poisson Equation in Any Space Dimensions
(Elsevier Ltd, 20090324)The finite difference discretization of the Poisson equation with Dirichlet boundary conditions leads to a large, sparse system of linear equations for the solution values at the interior mesh points. This problem is a ... 
Parallel studies for chemically reacting systems
(20090806)Parallel computing code can be applied to solve chemically reacting systems. In a well stirred chemical system, the number of molecules for each species can be solved by implicit tau method, and the histogram of the method ... 
On the Equivalence of Primal and Dual Substructuring Preconditioners
(Kent State University, 20090930)After a short historical review, we present four popular substructuring methods: FETI1, BDD, FETIDP, BDDC, and derive the primal versions to the two FETI methods, called PFETI1 and PFETIDP, as proposed by Fragakis ...