Mathematics Lecture Series, Fall 2012

Dr. Adnan Sabuwala

California State University, Fresno

“Derivatives, Finite Differences and Optimal Grids”

Friday, October 19, 2012

from 4:00 p.m. to 5:00 p.m.

Science 145

The derivative of a function, f’(x), is first introduced in calculus. In a differential equations class, these derivatives are used to model real-world phenomena. In this talk, we will look at a practical implementation of the derivative on a computer using finite difference methods. Traditional finite difference techniques using uniform grids for numerical solution of PDE's are slow and compute the solution over the entire problem domain. However, for receiver-targeted applications such as geophysical exploration, one wishes to compute faster solutions to PDE's at specific receiver locations with high accuracy. Spectrally matched optimal grids have been shown to achieve super exponential convergence for such problems. We will give an introduction to the method of computing spectrally matched optimal grids. We will also look at an application of these optimal grids to anisotropic problems.

For further information, please contact Dr. Tamas Forgacs at (559) 278-4907 or e-mail tforgacs@csufresno.edu.