# Hongkai Zhao : Can iterative method converge in a finite number of steps?

When iterative methods are used to solve a discretized linear system for partial differential equations, the key issue is how to make the convergence fast. For different type of problems convergence mechanism can be quite different. In this talk, I will present an efficient iterative method, the fast sweeping method, for a class of nonlinear hyperbolic partial differential equation, Hamilton-Jacobi equation, which is widely used in optimal control, geometric optics, geophysics, classical mechanics, image processing, etc. We show that the fast sweeping method can converge in a finite number of iterations when monotone upwind scheme, Gauss-Seidel iterations with causality enforcement and proper orderings are used. We analyze its convergence, which is very different from that for iterative method for elliptic problems. If time permit I will present a new formulation to compute effective Hamiltonians for homogenization of a class of Hamilton-Jacobi equations. Both error estimate and stability analysis will be shown.

**Category**: Applied Math and Analysis**Duration**: 01:34:34**Date**: March 12, 2012 at 4:25 PM**Views**: 114-
**Tags:**seminar, Applied Math And Analysis Seminar

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