Faculty Advisor

Robert P. Lipton

Faculty Advisor

Konstantin A. Lurie

Faculty Advisor

Bogdan M. Vernescu

Faculty Advisor

Nikos A. Gatsonis

Faculty Advisor

Domokos Vermes

Faculty Advisor

Arthur C. Heinricher


"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."


Worcester Polytechnic Institute

Degree Name



Mathematical Sciences

Project Type


Date Accepted





gradient fields, functionally graded materials, laminates, optimal design, Electrostatics, Dielectrics, Mathematical optimization