(Description of Seminar 10)
Nov. 3, 1997
On last wednesday, Dr. Joseph Kolibal gave us a lecture about Applying Mollifyers to Numerically Solved PDE's. Dr. Joseph Kolibal is a professor of Department of Mathematics, University of Southern Mississippi.
Dr. Kolibal first gave some introduction. He considered techniques applicable to filtering or smoothing noisy functions g. These can be subsumed within the theory of mollifyers.
Dr. Kolibal introduced the two-dimensional system of equations. He presented one dinensional model and the discretizations about it.
Approximations of functional derivatives are constructed through a process of mollification. The resultant functional approximations are analytic and are suitable for numerically solving partial differential equations. Since the derivatives are obtained analytically from a smooth approximation of the function, all derivatives at a point are available at any location in the domain during the numerical differentiation.
To demonstrate the workability of the concept, the technique is applied to a hyperbolic PDE, the De Laval nozzle problem in computational fluid dynamics.