This new course, created through the cooperation of the Center for Computational Research and the Departments of Chemical Engineering, Mathematics,and Mechanical and Aerospace Engineering, introduces the fundamental ideas of scientific computing on high performance architectures. These computers, and the efficient algorithms developed for them, are enabling realistic simulations of many complex physical phenomena. Computational Science is becoming a third method of science, complementing theoretical and experimental research. Indeed, the DOE has set up an ambitious plan to simulate all current and future nuclear weapons in the US arsenal! A good knowledge of Computational Science is rapidly becoming an indespensible tool for all scientists. UB has made a significant investment in setting up the CCR, currently one of the top 10 academic supercomputing centers.

During this second semester, we will concentrate on applications in computational science, including solving differential equations, Monte Carlo computations, molecular dynamics simulations, and Fourier transforms.
 
 

Prerequisites: HPCI, graduate standing, and and good programming skills in FORTRAN and/or C and/or C++.

Grading: Grades will be based on homework assignments (60%) and a term project (40%). The assignments will consist of several parts (e.g, write a serial code, then port it to a parallel environment), together with a 2-3 page written report. The term project will be a larger coding assignment, on a topic of your choice.

Textbook: There is no required textbook. We will make extensive use of on-line materials, some of which are listed below.

Links to Resources:  others will be posted during the semester
 Scientific Supercomputing by W. Schoenauer
 Computational Science e-book
 CCR Training Links
 CCR Links to Education sites  (including links from Dr. Patra's course)
  MGNet The Multigrid Net, which includes codes, tutorials, preprints, conferences and a world of good stuff.
 W. Briggs, A Multigrid Tutorial, a dead tree book presenting the elementary theory of multigrid. Recommended.
  Templates for the solution of linear systems  an html version of the book
 Jim Demmel's Multigrid lecture

Lectures:
Solving Boundary-Value Problems
Molecular Dynamics
Navier-Stokes solver
References on CFD and multi-fluid flows used in preparing lectures include: A Second-order Projection Method for Tracking Interfaces in Variable Density Incompressible Flows, An Adaptative Level Set Approach for Incompressible Two Phase Flows, Adaptative Mesh and Algorithm Refinement.

Bill Rider's page has links to work on CFD and interface tracking methods. Another good source for information is the CCSE page at LBL. Tryggvason's work was published in JCP vol.100 (1992), p25 and references therein.

FFT