This module teaches the basic principles of semi-classical transport simulation based on the time-dependent Boltzmann transport equation (BTE) formalism with performance considerations for parallel implementations of multi-dimensional transport simulation and the numerical methods for efficient and accurate solution of the BTE for both electronic and thermal transport using the simple finite difference discretization and the stable upwind method.
Many students taking a second course in linear algebra with a computational orientation find it very helpful to see an overview of concrete areas of application. This module contains two such applications. The first one is a general introduction to the Google PageRank algorithm showing why numerical eigenvalue computation is relevant.A second application is that of a spring-mass system with design updates. The focus is on solving eigenvalue and linear systems of equations using MATLAB.
CAChe software is used for computational chemistry. It is simple to use and is therefore suitable for educational endeavors. Different versions include molecular mechanics, semiempirical, and density functional theory (DFT) methods of calculation.
A pdf file that can be read using the free Abode Acrobat Reader or, for more functionality, with Acrobat Pro ($). The eBook's figures, equations, sections, chapters, index, table of contents, code listings, glossary, animations and executable codes (both Applets and Python programs) are linked, much like in a Web document. There are also links to video-based lectures covering most topics in the text, as well as to the slides used in the lectures. Section 1.2 of the text discusses how to use the various electronic features. Some movies are encapsulated into the text and some equations are linked to their xml forms (which can be imported into Maple or Mathematica for manipulation).
MUDPACK is a collection of vectorized portable Fortran 77/90 subprograms which efficiently solve linear elliptic Partial Differential Equations using multigrid iteration.
The N-Body problem has become an intricate part of the computational sciences, and there has been rise to many methods to solve and approximate the problem. The solution potentially requires on the order of calculations each time step, therefore efficient performance of these N-Body algorithms is very significant [5]. This work describes the parallelization and optimization of the Particle-Particle, Particle-Mesh (P3M) algorithm within GalaxSeeHPC, an open-source N-Body Simulation code. Upon successful profiling, MPI (Message Passing Interface) routines were implemented into the population of the density grid in the P3M method in GalaxSeeHPC. Each problem size recorded different results, and for a problem set dealing with 10,000 celestial bodies, speedups up to 10x were achieved. However, in accordance to Amdahl's Law, maximum speedups for the code should have been closer to 16x. In order to achieve maximum optimization, additional research is needed and parallelization of the Fourier Transform routines could prove to be rewarding. In conclusion, the GalaxSeeHPC Simulation was successfully parallelized and obtained very respectable results, while further optimization remains possible.
eTEACH is a vehicle for publishing coordinated multi-media instructional materials on the World Wide Web. Logically, an eTEACH presentation consists of digital streaming video, a coordinated "slide show," a table of contents, and possibly optional materials and links to external web sites.
Color numbers in Pascal's Triangle by rolling a number and then clicking on all entries that are multiples of the number rolled, thereby practicing multiplication tables, investigating number patterns, and investigating fractal patterns. Coloring Multiples in Pascal's Triangle is one of the Interactivate assessment explorers.
