Mathematics 655 Course Description

Advanced Topics in Numerical Analysis, Fall, 2007

The title of the course for this semester is "Parallel processing in scientific computing: Parallelism in Branch and Bound Algorithms for Optimization and in Partial Differential Equations."  We will be following our primary  text (Parallel and Distributed Computation: Numerical Methods by Bertsekas et al;) for the basics of parallel processing, and we will be doing assignments from that text;  we may also use Parallel Scientific Computing in C++ and MPI, George Em Karniadakis and Robert M. Kirby II, Cambridge Univ. Press, QA76.58 K37 2003, ISBN 0-521-81754-4.  This may occupy us for most of the Fall semester.

Along with exercises in the text, we will be doing "hands-on" work in an actual parallel environment:  The "bigred" cluster recently deployed at CACS.  This will require a knowledge of either C++ or FORTRAN 77.  We will cover in class MPI, the "Message Passing Interface" library, that will be used to effect execution on multiple processors.

Here is a motivational description for the course:

On computers or distributed systems of computers with more than one processor, numerical algorithms often need to be viewed in fundamentally different ways. However, creation of methods for such parallel architectures is becoming increasingly important. First, parallel and distributed systems are being used more and more to tackle otherwise intractable problems in applications of scientific computing; for such problems, the University of Louisiana's LITE installation and the State of Louisiana's LONI network have been developed.  Second, increased parallelism on multiple levels is occurring even in mass-produced computational equipment; this is evidenced, for example,
by Intel's "Core DUO" processors; the actual speed of each core is usually slower than earlier single-core chips, and the full speed of the chip cannot be attained for a particular application unless parallel algorithms are used.

Two scientific computing problems of research interest in the department will be considered in a parallel context:

  1. deterministic branch and bound algorithms for global optimization, and
  2. solution of systems of partial differential equations, such as might arise in three-dimensional fluid mechanics.

Although the course will focus on the numerical analysis and scientific computing, relevant elements of parallel programming languages such as MPI and PVM will be introduced. Experience on Louisiana's parallel processing systems will be gained.

Check the Moodle course for additional materials and information.

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