Credits -- 3 (2-1-0)
Term Offered -- Spring
- Description
-- - The term Computational
Scientist has been coined to describe scientists, engineers and
mathematicians who apply high-performance computational technology in
an innovative and essential way to advance the state of knowledge in
their discipline. In the areas of high performance computing and
numerical modeling, the effective computational scientist needs to have
command of an applied discipline and must be familiar with leading
edge computer architectures and algorithms. Also, visualization
techniques for the pre and post processing of model data are becoming
an essential tool in the area of computational science.
- Goal
-- - The goal of the course GS-511
is to enable students to develop skills required of an effective
computational scientist. Since the solution of systems of linear
equations is central to much of computational science, the GS-511 course
spends a good deal of time discussing efficient data structures and
solution methods for this important class of problems. Special
attention is given to sparse, banded systems of equations, such as
those arising in connection with the finite difference and finite
element methods. The course highlights the interplay between storage
considerations, algorithm convergence rate and CPU performance.
The matching of an algorithm and an architecture are given considerable
attention. The course focuses on the CRAY YMP architecture, but
students also compute on a Connection and a variety of workstations.
Introductory material on visualization and image processing is presented.
GS-511 is a 3 (2-1) credit course meeting twice per week with a credit
of computer laboratory.
- Topics
--
- Systems of Linear Equations Arising in Computational Science
- Iterative vs Direct Methods
- Jacobi, Gauss-Seidel and SOR: Convergence and Vectorization
- Conjugate Gradient Method
- Implementation of CG Method to Sparse, Banded Systems of Equations
- Preconditioners for CG Method
- Performance comparisons of Jacobi, GS, SOR, Red-Black ADI and CG
- Library Routines and Software Packages
- Monte Carlo Methods
- Visualization and Image Processing
Instructor -- D. Zachmann