Dear Colleagues,

We continue our Colloquium in the Math Department.

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Thursday, November 4, EMCS 422, 3:00 pm.

Pierre A. Gremaud,

Department of Mathematics,

North Carolina State University

(with Chris Kuster, the same school)

Numerical Methods for Stationary Hamilton-Jacobi Equations

Abstract

The Hamilton-Jacobi equations find their origin in Classical Mechanics.
They appear naturally in wave propagation problems, optimal Control,
level set formulations and countless other problems. In short, they are
ubiquitous in modern Applied Mathematics. Hamilton-Jacobi equations are
well understood theoretically (at least in the multidimensional scalar
case).

In this talk, we will start by briefly reviewing the history, range of
application and analysis of Hamilton-Jacobi equations. We will then turn
to numerical methods for such equations. Even though the underlying
problems maybe ones of propagation, discretized Hamilton-Jacobi
equations do not naturally lead to explicit methods (unlike hyperbolic
conservation laws for instance). Instead, discretization leads to
"general" nonlinear systems. While traditional nonlinear solvers (Newton
like methods) can always be used, in many cases "one pass" algorithms
can be designed and implemented, leading to tremendous savings. We will
review two such methods, Fast Marching and Fast Sweeping, present
generalizations of those methods to problems with obstacles and discuss
the relative performance of those algorithms.

The talk will be elementary in nature and aimed at the non experts.

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Boris P Belinskiy

Department of Mathematics, Dept. 6956

University of Tennessee at Chattanooga

Ph. (423) 425-4748