VIGRE seminar, fall 2000: Numerical Analysis

Instructors

Raytcho Lazarov, Joe Pasciak

Students enrolled

Woonjung Choi, Veselin Dobrev, Paul Dostert, Tzanio Kolev, Dukjin Nam, Yanqiu Wang (graduate mathematics students); Chun Park (graduate statistics student)

Description

The VIGRE course on numerical analysis focused on numerical algorithms and large scale scientific computation. The recent advances in computing power have allowed for the development of high fidelity, mathematically sophisticated models. The current state of the art in large scale scientific computation ultimately involves algorithms especially developed for execution on parallel computing platforms.
There were three major components in this course:

1. Methods and algorithms in scientific computing (including approximation methods utilizing finite difference, finite element, and spectral approximation);
2. Applications to physics and engineering, economics, biology, etc. in terms of partial differential equations;
3. Software tools, programming methodologies, and code development.

The first part of the course involved study and discussion of the most popular algorithms and methods in scientific computing. The second part of the course provided various mathematical applications while the third part of the course was related to a group project of developing codes called Aggie FEM and GLVIS. These are object oriented finite element and visualisation codes that include: parallel programming, mesh generation and visualisation tools and applications to electromagnetics, flows in porous media, elasticity, and potential problems.

Impact

The project was a definite success and benefitted all participating students. This code has been subsequently used in other research projects by some of the students from the class and other students from our department. In particular, the code was used to test various preconditioning strategies for problems of flows in porous media in highly heterogeneous and orthotropic media, partially funded by Saudi Aramco Oil Co. In addition, the visualisation code was used to provide graphics for S. Tomov's thesis.