Physical Sciences and Mathematics Commons^™

Optimal Control Of A Heat Flux In A Parabolic Partial Differential Equation, Katherine Renee Deaton

Masters Theses

We consider the problem of controlling the solution of a parabolic partial differential equation with non-homogeneous Neumann boundary conditions, taking the flux as the control. We take as our cost functional the sum of the L² norms of the control and the difference between the temperature distribution attained and the desired temperature profile. We establish the existence of an optimal control that minimizes the cost functional. The optimal control is characterized in a constructive way through the solution to the optimality system, which is the original problem coupled with an adjoint problem. We establish existence and uniqueness of the …

Graph Theory Based Routing Algorithms, Bo Wu

Masters Theses

In this thesis, we study two VLSI layout problems.

We investigate the Minimum-Bend Single Row Routing Problem in which the objective function is to minimize the number of doglegs (or blends) per net. Our approach uses a graph theoretic representation in which an instance of the Single Row Routing Problem is represented by three graphs, an overlap graph, a containment graph and an interval graph. Using this graph representation, we develop three algorithms for minimum-bend single row routing problem.

We present a three-layer over-the-cell router (ICR-3) for the standard cell design style based on a new cell model which assumes …