Index Catalog // ScholarsArchive@OSU

Polynomial Chaos Expansions for Random Ordinary Differential Equations

Creator:: McKenzie, Brian
Abstract:: We consider numerical methods for finding approximate solutions to Ordinary Differential Equations (ODEs) with parameters distributed with some probability by the Generalized Polynomial Chaos (GPC) approach. In particular, we consider those with forcing functions that have a random parameter in both the scalar and vector case. We then consider linear...
Resource Type:: Capstone Project
Full Text:: Polynomial Chaos Expansions for Random Ordinary

Analysis of fourth order numerical methods for the simulation of electromagnetic waves in dispersive media

Creator:: Henderson, Scott Edward
Abstract:: In this thesis, we investigate the problem of simulating Maxwell's equations in dispersive dielectric media. We begin by explaining the relevance of Maxwell's equations to 21st century problems. We also discuss the previous work on the numerical simulations of Maxwell's equations. Introductions to Maxwell's equations and the Yee finite difference...
Resource Type:: Masters Thesis
Full Text:: Numerical Methods for the Simulation of Electromagnetic Waves in Dispersive Media Abstract approved

Operator splitting methods for Maxwell's equations in dispersive media

Creator:: Keefer, Olivia A.
Abstract:: Accurate modeling and simulation of wave propagation in dispersive dielectrics such as water, human tissue and sand, among others, has a variety of applications. For example in medical imaging, electromagnetic waves are used to interrogate human tissue in a non-invasive manner to detect anomalies that could be cancerous. In non-destructive...
Resource Type:: Masters Thesis
Full Text:: be considered in this thesis for modeling electromagnetic wave propagation in polar dispersive

Electromagnetic Inverse Problem for Relaxation Time Distribution in the Time-Domain

Creator:: Armentrout, Megan
Abstract:: We consider wide bandwidth electromagnetic pulse interrogation problems for the determination of dielectric response parameters in complex dispersive materials. We couple Maxwell’s equations with an auxiliary ODE modeling dielectric polarization. A problem of particular interest is to identify parameters in a standard polarization model (e.g., Debye or Lorentz) using time-domain...
Resource Type:: Capstone Project
Full Text:: generalized Polynomial Chaos in the forward problem. 1 Introduction Electromagnetic (EM) waves are a part of

A Sequential Operator Splitting Method for Electromagnetic Wave Propagation in Dispersive Media

Creator:: Bokil, Vrushali and Leung, Aubrey
Abstract:: In this report we consider the Debye model along with Maxwell's equations (Maxwell-Debye) to model electromagnetic wave propagation in dispersive media that exhibit orientational polarization. We construct and analyze a sequential operator splitting method for the discretization of the Maxwell-Debye system. Energy analysis indicates that the operator splitting scheme is...
Resource Type:: Undergraduate Thesis
Full Text:: A Sequential Operator Splitting Method for Electromagnetic Wave

High-Order Staggered Finite Difference Methods for Maxwell's Equations in Dispersive Media

Creator:: Bokil, Vrushali A. and Gibson, Nathan L.
Abstract:: We study the stability properties of, and the phase error present in, several higher order (in space) staggered finite difference schemes for Maxwell's equations coupled with a Debye or Lorentz polarization model. We present a novel expansion of the symbol of finite difference approximations, of arbitrary (even) order, of the...
Resource Type:: Technical Report
Full Text:: . 1 Introduction The computational simulation of electromagnetic interrogation problems, for the

Water content and electrical conductivity profile measurements for dispersive media using enhanced time domain and frequency domain models

Creator:: Flugstad, Benjamin A.
Abstract:: Water conservation and water quality are rapidly increasing in importance in all areas of the world. The ability to accurately measure soil water content and salinity, over a wide variety of conditions, is key to meeting this need. A set of forward prediction models and waveform interpretation algorithms to extract...
Resource Type:: Dissertation
Full Text:: for Dispersive Media using Enhanced Time Domain and Frequency Domain Models AN

Three dimensional electromagnetic FDTD simulation of general lossy structures with nonuniform grid spacing

Creator:: Falconer, Maynard C.
Abstract:: A new second order accurate nonuniform grid spacing technique which does not depend on supraconvergence is developed for Finite Difference Time Domain (FDTD) simulation of general three dimensional structures. The technique is useful for FDTD simulations of systems which require finer details in small regions of the simulation space by...
Resource Type:: Dissertation
Full Text:: using the FDTD method has already been performed by the electromagnetic community for microwave

Qualitative Analysis of Maxwell-Duffing Models in Nonlinear Optics

Creator:: Tro, Sara K.
Abstract:: In this thesis we analyze a model for Kerr optical materials consisting of Maxwell's equations along with the dispersive Duffing model. We consider Duffing models with cubic and quintic polynomial nonlinearities. We assume a traveling wave solution to this nonlinear electromagnetic system and analyze it using the theory of dynamical...
Resource Type:: Honors College Thesis
Full Text:: the dispersive Duffing model. We consider Duffing models with cubic and quintic polynomial

Multiscale Methods and Energy Stable Discretizations for Maxwell’s Equations in Linearand Nonlinear Materials

Creator:: Sakkaplangkul, Puttha
Abstract:: In this dissertation, we introduce a family of fully discrete finite difference time-domain (FDTD) methods for Maxwell’s equations in linear and nonlinear materials. Onecategory of methods is constructed using multiscale techniques involving operator splittings. We present the sequential splitting scheme, the Strang Marchuk splitting scheme,the weighted sequential splitting scheme including...
Resource Type:: Dissertation
Full Text:: operator splitting schemes based on energy techniques for Maxwell’s equations in linear non-dispersive and

ScholarsArchive@OSU

Polynomial Chaos Expansions for Random Ordinary Differential Equations

Analysis of fourth order numerical methods for the simulation of electromagnetic waves in dispersive media

Operator splitting methods for Maxwell's equations in dispersive media

Electromagnetic Inverse Problem for Relaxation Time Distribution in the Time-Domain

A Sequential Operator Splitting Method for Electromagnetic Wave Propagation in Dispersive Media

High-Order Staggered Finite Difference Methods for Maxwell's Equations in Dispersive Media

Water content and electrical conductivity profile measurements for dispersive media using enhanced time domain and frequency domain models

Three dimensional electromagnetic FDTD simulation of general lossy structures with nonuniform grid spacing

Qualitative Analysis of Maxwell-Duffing Models in Nonlinear Optics

Multiscale Methods and Energy Stable Discretizations for Maxwell’s Equations in Linearand Nonlinear Materials

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