Numerical Analysis - Scientific Computing Courses

MA 5310 - Computational Methods in Applied Sciences I

Course Description: First semester of a three-semester computational methods series. Review of iterative solutions of linear and nonlinear systems of equations, polynomial interpolation/approximation, numerical integration and differentiation, and basic ideas of Monte Carlo methods. Comparison of numerical techniques for programming time and space requirements, as well as convergence and stability.

Prerequisites: Math 3310 and COSC 1010. Identical to COSC 5310, CHE 5140, ME 5140, and CE 5140. (3 hours).

 

MA 5340 - Computational Methods in Applied Sciences II

Course Description: Second semester of a three-semester computational methods series with emphasis on numerical solution of differential equations. Topics include explicit and implicit methods, methods for stiff ODE problems, finite difference, finite volume, and finite element methods for time-independence PDEs semi/fully discrete methods for time-dependent PDEs.

Prerequisites: None. Indentical to COSC 5340. (3 hours)

 

MA 5490 - Parallel Computing I

Course Description: A one semester self contained course on parallel computing. Review of parallel architectures, hardware accelerators, programming paradigms, communications methods, applications, algorithms, how to buy or build a supercomputer, and how different scales of parallelism affect performance.

Prerequisites: Permission of the instructor.

 

MA 5490 - Parallel Computing II

Course Description: A second semester course on parallel computing. We will apply knowledge of parallel architectures, hardware accelerators, programming paradigms, communications methods, applications, algorithms, and how different scales of parallelism affect performance to design and implement an application in parallel on a tradition cluster and a nontraditional GP-GPU cluster.

Prerequisites: Permission of the instructor.

 

MA 5490 - Multilevel, Multigrid, and Multiscale Methods

Course Description: This course will comprehensively cover algorithms for numerically solving partial differential equations using multigrid methods (or multilevel methods when applied to a problem that is not grid based). Theory and how the algorithms really work in practice will be emphasized equally for a wide range of problems. Geometric and algebraic multigrid algorithms will be included. We will also cover multiscale methods as a form of a multilevel algorithm for problems in which different scales provide different and useful information about the solution to a problem. For example, many problems in energy are multiscale problems primarily and may also use traditional multigrid methods as well. This course is open to Graduate and Undergraduate students. Depending on the background of the students, we may study nuclear reactor core designs for third+ and fourth generation reactors. This is an emerging research area again due to the large number of reactors that are in the process of being approved in various countries (U.S., China, India, etc.) and the almost complete lack of trained people in the field.

Prerequisites: Permission of the instructor.

 

Cheers,
Craig C. Douglas

Last modified: