Hongkai Zhao (UC Irvine)

Hamilton-Jacobi (HJ) equation is a class of nonlinear hyperbolic partial differential equations that have wide applications in optimal control, geometric optics, image processing and computer graphics, etc. In this talk I will present an efficient iterative method, the fast sweeping method, for computing the numerical solution of static convex HJ equations on both structured and unstructured meshs. Convergence, error estimate and optimal complexity will be shown. Every iterative method converges for a reason. The fast sweeping method can converge in a finite number of iterations that is independent of mesh size. I will explain the two most crucial mechanisms, ordering and causality enforcement during Gauss-Seidel iterations, for the fast convergence of fast sweeping method. Applicability of the fast sweeping method to other hyperbolic type problems will also be discussed.