Mathematics faculty and graduate students are invited to attend the PhD Preliminary Examination of Justin O’Connor.

Advisor:  Dr. Wolfgang Bangerth

Committee:  Dr. Patrick Shipman, Dr. James Liu, Dr. Christopher Weinberger

Topology Optimization asks what shape is best to perform some task governed by a partial differential equation (PDE). This has many far-reaching applications related to computer-generated design. In recent years, it has been shown that solutions giving better objective values are found by simultaneously solving the governing PDE and finding an optimization step. This Simultaneous ANalysis and Design (SAND) technique is extremely computationally expensive, and therefore is currently not used in practice. In this talk, I consider a variety of modern nonlinear optimization techniques that allow for a faster SAND solve. These techniques culminate in a large, sparse, and indefinite linear system. I discuss preconditioning methods for solving this system and demonstrate the feasibility of solving real-world applications using SAND. Finally, I propose several continuations to my dissertation, including further improvements for my preconditioner, and implementation of other large-scale examples