Title page for ETD etd-0616100-180816

Document Type dissertation

Author Name Velo, Ani P.

Email Address aa0349 at exmail.usma.army.mil

URN etd-0616100-180816

Title Optimal Design of Gradient Fields with Applications to Electrostatics

Degree PhD

Department Mathematical Sciences

Advisors
Robert P. Lipton, Advisor
Konstantin A. Lurie, Committee Member
Bogdan M. Vernescu, Committee Member
Nikos A. Gatsonis, Committee Member
Domokos Vermes, Committee Member
Arthur C. Heinricher, Committee Member

Keywords
gradient fields
functionally graded materials
laminates
optimal design

Date of Presentation/Defense 2000-04-21

Availability unrestricted

Abstract
In this work we consider an optimal design problem formulated on a two dimensional domain filled with two isotropic dielectric materials. The objective is to find a design that supports an electric field which is as close as possible to a target field, under a constraint on the amount of the better dielectric.
In the case of a zero target field, the practical purpose of this problem is to avoid the so called dielectric breakdown of the material caused due to a relatively large electric field.
In general, material layout problems of this type fail to have an optimal configuration of the two materials. Instead one must study the behavior of minimizing sequences of configurations. From a practical perspective, optimal or nearly optimal configurations of the two materials are of special interest since they provide the information needed for the manufacturing of optimal designs.
Therefore in this work, we develop theoretical and numerical means to support a tractable method for the numerical computation of minimizing sequences of configurations and illustrate our approach through numerical examples.
The same method applies if we were to replace the electric field by electric flux, in our objective functional. Similar optimization design problems can be formulated in the mathematically identical contexts of electrostatics and heat conduction.

Files
velo.pdf

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Document Type	dissertation
Author Name	Velo, Ani P.
Email Address	aa0349 at exmail.usma.army.mil
URN	etd-0616100-180816
Title	Optimal Design of Gradient Fields with Applications to Electrostatics
Degree	PhD
Department	Mathematical Sciences
Advisors	Robert P. Lipton, Advisor Konstantin A. Lurie, Committee Member Bogdan M. Vernescu, Committee Member Nikos A. Gatsonis, Committee Member Domokos Vermes, Committee Member Arthur C. Heinricher, Committee Member
Keywords	gradient fields functionally graded materials laminates optimal design
Date of Presentation/Defense	2000-04-21
Availability	unrestricted
Abstract In this work we consider an optimal design problem formulated on a two dimensional domain filled with two isotropic dielectric materials. The objective is to find a design that supports an electric field which is as close as possible to a target field, under a constraint on the amount of the better dielectric. In the case of a zero target field, the practical purpose of this problem is to avoid the so called dielectric breakdown of the material caused due to a relatively large electric field. In general, material layout problems of this type fail to have an optimal configuration of the two materials. Instead one must study the behavior of minimizing sequences of configurations. From a practical perspective, optimal or nearly optimal configurations of the two materials are of special interest since they provide the information needed for the manufacturing of optimal designs. Therefore in this work, we develop theoretical and numerical means to support a tractable method for the numerical computation of minimizing sequences of configurations and illustrate our approach through numerical examples. The same method applies if we were to replace the electric field by electric flux, in our objective functional. Similar optimization design problems can be formulated in the mathematically identical contexts of electrostatics and heat conduction.
Files	velo.pdf