**Fast, accurate, and robust integral equation-based design and simulation tools**

**Speaker:** Michael O'Neil, PhD

**Series:** Other Events

**Location:**
J223 Equad

**Date/Time: **Friday, February 22, 2013, 1:30 p.m.
- 2:30 p.m.

**Abstract:**

Abstract: If the future of scientific computing and computational engineering lies in "design by simulation", it will require not only that a single problem be solved accurately and rapidly, but that an entire sequence of problems be solved, with varying geometry, material parameters, etc. Two trends over the last twenty years have allowed problems to be addressed which were previously thought to be intractable. First is the advance in high-performance computing environments (now including multi-core, GPU-based, and distributed architectures). Second, and equally important, is the development of numerical methods that allow for a vast increase in the number of degrees of freedom which can be considered. The fast multipole method, for example, has led to integral equation solvers whose cost grows only linearly with the number of unknowns. In this talk, I will give an overview of the analytical and numerical foundations of methods that will permit the construction of fast, high-order accurate, and robust methods that can be used in a variety of problems in science and engineering. Critical issues include the derivation of well-conditioned integral equation formulations for the governing PDE, high-order geometry representations, accurate quadrature rules for singular functions, and suitable fast algorithms. We will touch on the application of these techniques to problems drawn from classical mathematical physics, including acoustics, elasticity, electromagnetics, and heat flow.