# Graduate Student / Postdoc Seminar

#### Integral equation-based fast solvers for simulation and design

**Speaker:**
Mike O'Neil, Courant Institute of Mathematical Sciences

**Location:**
Warren Weaver Hall 1302

**Date:**
Friday, March 29, 2019, 1 p.m.

**Synopsis:**

In various areas of classical mathematical physics, for example electromagnetic wave propagation, heat diffusion, and incompressible fluid flow, the underlying model agrees very well with experimental results and the governing PDEs have been mathematically well-researched and understood. The main roadblocks to high-fidelity computational engineering design are mostly algorithmic and computational. In this talk we will give an overview of the mathematical and numerical techniques required in order to solve PDEs from various fields of classical mathematical physics using integral equations. The talk will cover topics including (1) derivation of integral equations, (2) computational geometry, (3) high-order quadrature and function approximation, and (4) fast solvers for dense, structured matrices. Some recent results in high-order meshing algorithms, electromagnetics, and plasma physics/fusion will be detailed.