CSI 801/INFT814

Foundations of Computational Science

This course will be about scientific computation, particularly on parallel computers. The term computational science to me implies the juxtaposition and joining of a natural science such as physics, chemistry, mathematics or statistics with computation. The idea is that computation forms a fundamental tool in the evolution of the science. Scientific computation on the other hand focuses on computational techniques used in the computational science. As their names imply, computational science is about science while scientific computation is about computing. This course will be about the computing in service to science.

Three books will be used:

My plan is to have three segments. The first three sessions will be devoted to development of some practical skills with UNIX, C, the parallel extensions to FORTRAN and C, architecture of the Intel iPSC/2 and the Intel Paragon XP/S, and some programming paradigms. The next ten sessions will be presented seminar style by students in the class according to the outline below. The last three sessions will involve some guest lectures by a statistician, a biologist and a fluid dynamicist on their use of scientific computation.

The syllabus for the student lectures (seminar) will be as follows:

Session 1

Chapter 3 Parallel and Vector Computing, Sci. Comp.
- 3.1 Parallel and Vector Computers
- 3.2 Basic Concepts in Parallel Computing
- 3.3 Matrix Multiplication
Chapter 3 Hardware and Operating Systems Models, Para. Prog.

Session 2

Chapter 4 Processes, Shared Memory, and Simple Parallel Programs, Para. Prog.
Chapter 5 Basic Parallel Programming Techniques, Para. Prog.

Session 3

Chapter 7 Introduction to Scheduling: Nested Loops, Para. Prog.
Chapter 8 Overcoming Data Dependencies, Para. Prog.

Session 4

Chapter 9 Scheduling Summary, Para. Prog.
Chapter 10 Linear Recurrence Relations -- Backwards Dependencies, Para. Prog.
Chapter 11 Performance Tuning, Para. Prog.

Session 5

Chapter 4 Polynomial Approximation, Sci. Comp.
- 4.1 Taylor Series, Interpolation and Splines
- 4.2 Least Squares Approximations
- 4.3 Application to Root Finding
Chapter 5 Continuous Problems Solved Discretely, Sci. Comp.
- 5.1 Numerical Integration

Session 6

Chapter 5 Continuous Problems Solved Discretely, Sci. Comp.
- 5.2 Initial Value Problems
- 5.3 Boundary Value Problems
- 5.4 Space and Time
- 5.5 The Curse of Dimensionality

Session 7

Chapter 6 Direct Solutions of Linear Equation Comp
- 6.1 Gaussian Elimination
- 6.2 Errors in Gaussian Elimination
- 6.3 Other Factorizations

Session 8

Chapter 7 Parallel Direct Method Comp
- 7.1 Basic Methods
- 7.2 Other Organizations of Factorization
- 7.3 Banded and Tridiagonal Systems

Session 9

Chapter 8 Iterative Methods, Sci. Comp.
- 8.1 Relaxation-type Methods
- 8.2 Parallel and Vector Implementations
- 8.3 The Multigrid Method

Session 10

Chapter 9 Conjugate Gradient-Type Methods, Sci. Comp.
- 9.1 The Conjugate Gradient Method
- 9.2 Preconditioning
- 9.3 Nonsymmetric and Nonlinear Problems

The abbreviations above are as follows:

Sci. Comp.: Scientific Computing: An Introduction with Parallel Computing by Gene Golub and James M. Ortega
Para. Prog..: Introduction to Parallel Programming by Steven Brawer

The book, Scientific Computing and Differential Equations by Gene Golub and James M. Ortega, will be used as a backup source to the other Golub and Ortega book.