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Filtering by: Alternative title ssim Polynomial Chaos for Dispersive Electromagnetics Remove constraint Alternative title ssim: Polynomial Chaos for Dispersive Electromagnetics Academic Affiliation Mathematics Remove constraint Academic Affiliation: Mathematics Language English [eng] Remove constraint Language: English [eng]

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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
Analysis of Stability and Dispersion in a Finite Element Method for Debye and Lorentz Dispersive Media

Creator:

Banks, H. T., Bokil, V. A., and Gibson, N. L.

Abstract:

We study the stability properties of, and the phase error present in, a finite element scheme for Maxwell’s equations coupled with a Debye or Lorentz polarization model. In one dimension we consider a second order formulation for the electric field with an ordinary differential equation for the electric polarization added...

Resource Type:

Article

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for Debye and Lorentz Dispersive Media H. T. Banks∗ Center for Research in Scientific Computation
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
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
Compatible Discretizations for Maxwell's Equations with General Constitutive Laws

Creator:

McGregor, D. A.

Abstract:

In this thesis we construct compatible discretizations of Maxwell's equations. We use the term compatible to describe numerical methods for Maxwell's equations which obey many properties of vector Calculus in a discrete setting. Compatible discretizations preserve the exterior Calculus ensuring that the divergence of the curl and the curl of...

Resource Type:

Dissertation

Full Text:

essence, these laws will relate various electromagnetic variables to one another. We consider for the
Virtual Element Methods for Magnetohydrodynamics on General Polygonal and Polyhedral Meshes

Creator:

Naranjo, Sebastián

Abstract:

The aim of this dissertation is to construct a virtual element method (VEM) for models in magneto-hydrodynamics (MHD), an area that studies the behavior and properties of electrically conducting ﬂuids such as a plasma. MHD models are a coupling of the Maxwell’s equations for electromagnetics and models for ﬂuid ﬂow....

Resource Type:

Dissertation

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electromagnetics and models for fluid flow. First we consider a simplified resistive MHD sub- model where we

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Academic Affiliation

Mathematics[remove]11

Advisor

Bokil, Vrushali A.4
Gibson, Nathan L.4
Bokil, Vrushali1

Commencement Year

Commencement Year range begin – Commencement Year range end

Current results range from 2009 to 2022

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Unknown 3

Committee Member

Faridani, Adel2
Gibson, Nathan L.2
Gyrya, Vitaliy2
Higdon, Robert L.2
Peszynska, Malgorzata2
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Creator

Armentrout, Megan1
Banks, H. T.1
Bokil, V. A.1
Bokil, Vrushali1
Bokil, Vrushali A.1
more Creators »

Contributor

Bokil, Vrushali1
Gibson, Nathan L.1
Woodside, C. R.1

Date

Date range begin – Date range end

Current results range from 2008 to 2022

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Decade

2020-20292
2010-20197
2000-20092

Degree Field

Mathematics9

Degree Level

Doctoral4
Master's4
Bachelor's1

Degree Name

Doctor of Philosophy (Ph.D.)4
Master of Science (M.S.)4
Bachelor of Arts (B.A.)1

File Format

pdf1

Language

English [eng][remove]11

License

All rights reserved6

Non-Academic Affiliation

Oregon State University. Graduate School4

Peer Reviewed

No10

Resource Type

Dissertation4
Capstone Project2
Masters Thesis2
Article1
Technical Report1
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Rights Statement

In Copyright8
Copyright Not Evaluated3

Subject

Electromagnetic waves -- Mathematical models2
Magnetohydrodynamics2
Maxwell equations2
Numerical analysis2
Dielectrics1
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