Numerical Analysis - Scientific Computing
Professor Craig C. Douglas

http://www.mgnet.org/~douglas/Classes/na-sc

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 basics (round off errors and matrix algebra review), finite differences and Taylor expansions, solution of linear systems of equations (Gaussian elimination variations (tridiagonal, general, and sparse matrices), iterative methods (relaxation and conjugate gradient methods), and overdetermined systems (least squares)), nonlinear equations (root finding of functions), interpolation and approximation (polynomial, Lagrange, Hermite, piecewise polynomial, Chebyshev, tensor product methods, and least squares fit), numerical integration (traditional quadrature rules and automatic quadrature rules), and one other topic (simple optimization methods, Monte-Carlo, etc.).

Prerequisites

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

Taught at and When

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. Identical to COSC 5340. (3 hours)

Taught at and When

MA 5345 - Computational Methods in Applied Sciences III

Course Description

Third semester of a three-semester computational methods series. The emphasis is on the numerical solution of problems displaying sharp fronts and interfaces (nonlinear conservation laws, Hamilton-Jacobi equations).

Prerequisites

None. Identical to COSC 5345. (3 hours)

Taught at and When

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.

Taught at and When

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.

Taught at and When

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.

Taught at and When

Perspective on Informatics 2 - Multigrid Methods and Nonconforming Finite Element Methods

Course Description

This course will cover finite element and finite difference methods to solve partial differential equations. In the first half of the course, multigrid methods (geometric and algebraic) will be covered. In the second half of the course, nonconforming finite element methods will be covered. Students will be expected to try numerical experiments based on the lectures.

Prerequisites

Students should be familiar with advanced calculus and numerical linear algebra.

Taught at and When

Cheers,
Craig C. Douglas

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