Browsing by Department "Computational and Applied Mathematics"
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Adaptive multiscale modeling of polymeric materials using goaloriented error estimation, Arlequin coupling, and goals algorithms
(200805)Scientific theories that explain how physical systems behave are described by mathematical models which provide the basis for computer simulations of events that occur in the physical universe. These models, being only ... 
Analysis of the discontinuous Galerkin method applied to collisionless plasma physics
(2007)Two discontinuous Galerkin methods (DG), the discontinuous flow upwind Galerkin (DFUG) and discontinuous flow upwind GalerkinNonsymmetric Interior Penalty Galerkin (DFUGNIPG) methods, are proposed to approximate the ... 
Boundary/finite element meshing from volumetric data with applications
(2005)The main research work during my Ph.D. study is to extract adaptive and quality 2D (triangular or quadrilateral) meshes over isosurfaces and 3D (tetrahedral or hexahedral) meshes with isosurfaces as boundaries directly ... 
Computational modeling and realtime control of patientspecific laser treatment of prostate cancer
(200805)Hyperthermia based cancer treatments delivered under various modalities have the potential to become an effective option to eradicate the disease, maintain functionality of infected organs, and minimize complications and ... 
A conservative deterministic spectral method for rarefied gas flows
(200808)The mathematical analysis of the Boltzmann equation for a wide range of important models is well developed. It describes physical phenomena which are often of great engineering importance (in aerospace industry, semiconductor ... 
Discontinuous Galerkin finite element methods applied to twophase, airwater flow problems
(2005)A set of discontinuous Galerkin (DG) finite element methods are proposed to solve the airwater, twophase equations arising in shallow subsurface flow problems. The different timesplitting approaches detailed incorporate ... 
Essays on derivatives pricing in incomplete financial markets
(200712)This dissertation is a contribution to the valuation and risk management of derivative securities in incomplete financial markets. It consists of two parts dedicated to two distinct valuation methodologies. In the first ... 
Fast multiscale methods for lattice equations
(2002)The thesis concerns multiscale analysis of equations defined on very large lattices. A new method for model reduction that allows the resolution scale to vary with spatial position is presented. It leads to fast numerical ... 
Finite element methods in linear poroelasticity: theoretical and computational results
(2005)Linear Poroelasticity refers to fluid flow within a deformable porous medium under the assumption of relatively small deformations. Some of the areas that are being modeled with the equations of linear poroelasticity ... 
Fully automatic hpadaptivity for acoustic and electromagnetic scattering in three dimensions
(200705)We present an algorithm for fully automatic hpadaptivity for finite element approximations of elliptic and Maxwell boundary value problems in three dimensions. The algorithm automatically generates a sequence of coarse ... 
Indifference valuation in nonreduced incomplete models with a stochastic risk factor
(200712)This work contributes to the methodology of valuation of financial derivative contracts in an incomplete market. It focuses on a special type of incompleteness caused by the presence of a nontraded stochastic risk factor, ... 
Integration of hpadaptivity with a two grid solver: applications to electromagnetics
(2004)James Clerk Maxwell published in A Treatise on Electricity and Magnetism (1873) a set of partial differential equations governing the electromagnetic (EM) phenomena. Since then, a variety of numerical methods have ... 
Isogeometric analysis and numerical modeling of the fine scales within the variational multiscale method
(200708)This work discusses isogeometric analysis as a promising alternative to standard finite element analysis. Isogeometric analysis has emerged from the idea that the act of modeling a geometry exactly at the coarsest levels ... 
Isogeometric analysis of turbulence and fluidstructure interaction
(2006)This work puts Isogeometric Analysis, a new analysis framework for computational engineering and sciences, on a firm mathematical foundation. FEMlike theory is developed in which optimal in h approximation properties ... 
Multiscale basis optimization for Darcy flow
(200705)Simulation of flow through a heterogeneous porous medium with finescale features can be computationally expensive if the flow is fully resolved. Coarsening the problem gives a faster approximation of the flow but loses ... 
Multiscale modeling using goaloriented adaptivity and numerical homogenization
(200908)Modeling of engineering objects with complex heterogeneous material structure at nanoscale level has emerged as an important research problem. In this research, we are interested in multiscale modeling and analysis of ... 
Numerical analysis of the representer method applied to reservoir modeling
(2006)The representer method is a data assimilation scheme that has received attention in the traditionally “datarich” fields of oceanography and meteorology. Now, advances in instrumenting and imaging subsurface reservoirs ... 
Numerical modeling of Stokesian emulsions
(2002)The principle objective of this dissertation was to develop a fast solution method for the accurate large scale modeling of fluid dynamics problems involving emulsions. The objective has been achieved by combining ...