Shodor

Curricular materials designed to teach parallel computational modeling to undergraduate or graduate students in science and other STEM disciplines. The module begins with the construction of a cellular automaton model of microbial biofilms using Mathematica. This model is then re-implemented with C and parallelized using MPI.

This module introduces the N-body problem, which seeks to account for the dynamics of systems of multiple interacting objects. Galaxy dynamics serves as the motivating example to introduce a variety of computational methods for simulating change and criteria that can be used to check for model accuracy. Finally, the basic issues and ideas that must be considered when developing a parallel implementation of the simulation are introduced.

The second of three modules, this module dives more deeply into the world of HPC and parallel computing. The primary topics explored are: Shared Memory Multithreading; Distributed Multiprocessing; Applications and Types of Parallelism; and Multicore Madness.

Many computational science models involve matrices. This module will provide a foundation for understanding matrices and some of their operations with examples from population dynamics and will provide background material for other computational science modules. The module will also have a discussion of the importance of matrices in many models that employ high performance computing. The model will have two accompanying tutorials. One will include some of the basics of MPI. The other will provide an introduction to matrices in Mathematica along with Grid Mathematica.

This module teaches: 1) How to approximate the area under a curve using a Riemann sum, 2) how approximating the area under a curve is used in solutions to scientific problems, 3) how to implement parallel code for Area Under a Curve (including versions that use shared memory via OpenMP, distributed memory via the Message Passing Interface (MPI), and hybrid via a combination of MPI and OpenMP), 4) how to measure the performance and scaling of a parallel application in multicore and manycore environments, and 5) how Area Under a Curve falls into the MapReduce "dwarf" (a class of algorithms that have similar communication and computation patterns). Upon completion of this module, students should be able to: 1) Understand the importance of approximating the area under a curve in modeling scientific problems, 2) Design a parallel algorithm and implement it using MPI and/or OpenMP, 3) Measure the scalability of a parallel code over multiple or many cores, and 4) Explain the communication and computation patterns of the MapReduce dwarf. It is assumed that students will have prerequisite experience with C or Fortran 90, *nix systems, and modular arithmetic.