N-body Methods and Particle Simulations

CSI 761 - Spring 1997

John Wallin


Assignment 2 is on-line!

Assignment 3 is online!

Assignment 4 is on-line!

Introduction

During this class, you will be introduced into the methods used to solve the N-body problem using numerical simulations. The material presented will include topics in numerical methods, computer science, physics, and N-body applications.

Textbooks and Course Materials

The main textbooks for this course are Computer Simulations Using Particles by R.W. Hockney and J.W. Eastwood and Code Complete by S. McConnell. The second book is an excellent handbook for software engineering. We will be covering the material in this book as part of the lectures through the semester. Since the principle focus of the Hockney and Eastwood book is particle-mesh simulations, I will be taking some lecture material from:

  • Classical Dynamics by J.B. Marion
  • Galactic Dynamics by J. Binney and S. Tremaine
  • Numerical Recipes by W.H. Press, B.R. Flannery, S.A. Teukolsky, and W.T. Vettering
  • Computer Simulations of Liquids by Allen and Tildesley
  • I will also be using selected materials from a course packet which will be available through the copy center. Additional material will be on the WWW through Mosaic.

    Evaluation

    The grade for this class will be based on your performance on programming projects, your semester paper, and a final exam. You will choose the subject of the research paper subject to my approval. The final exam will be a "take-home" based on material covered in lectures, homework, and computer projects.

    Computer projects

    During the semester, you will be writing a number of code segments. You may use Fortran, C, or C++ as a programming language. The evaluation of the codes will be based on standards discussed in class.

    Office Information

    Science and Tech I, Room 109
    703-993-3617
    Email: jwallin@gmu.edu
    http://galileo.gmu.edu/jwbio.html



    Lecture Schedule


    Lecture 1: 1/23/97

    Classical Mechanics and particles
    Variational principles, Lagrangian, conservation relationships
    Marion Chapters 6-8

    McConnell 1-52 (Laying the Foundation)


    Lecture 2: 1/30/97

    Structured Programming , Visualization, and Chaos
    Programming Standards and Techniques, Visualization tools,
    Chaotic Dynamics
    CSEP Server, Hockney and Eastwood

    McConnell 53-170 (Design)


    Lecture 3: 2/6/97

    Direct Summation
    The Brute Force N-body Solution, programming standards
    Hockney and Eastwood, Papers

    McConnell 53-170 (Design)


    Lecture 4: 2/13/97

    Initial Conditions of Particle Codes
    Statistical Mechanics, Distribution functions, and Initialization
    Binney and Tremaine + Allen and Tildseley

    McConnell, 267-298 (Data)


    Lecture 5: 2/20/97

    ODEs
    Numerical Solution to Ordinary Differential Equations
    CSEP Server, Numerical Recipies

    McConnell, 399-556 (Constant Considerations)


    Lecture 6: 2/27/97

    Linear algebra and data structures
    Solving complex linear systems, basic data structuring including trees
    CSEP

    McConnell, 399-556 (Constant Considerations)


    Lecture 7: 3/6/97

    Solving PDE -Elliptical Equations
    Mesh relaxation, Matrix Methods
    CSEP, Hockey and Eastwood

    McConnell, 557-650 (Quality Improvement)


    Spring Break: 3/13/97


    Lecture 8: 3/20/97

    The Fast Fourier Transform and Elliptical PDE's

    McConnell, 557-650 (Quality Improvement)


    Lecture 9: 3/27/97

    Particle Mesh and P3M Codes I
    Mapping Particles on Grids, Interpolating Forces
    Tracing Particle Trajectories through a Force Field
    Hockey and Eastwood

    McConnell, 651-754 (Final Steps)


    Lecture 10: 4/3/97

    Particle Mesh and P3M Codes I
    Creating a Particle-Based Force Field
    P3M codes
    Hockey and Eastwood

    McConnell, 651-754 (Final Steps)


    Lecture 11 : 4/10/97

    Hierarchical Tree Codes
    Analytic multipole expansion
    Hernquist code

    McConnell, 755-792 (Craftsmanship)


    Lecture 12: 4/17/97


    Lecture 13: 4/24/97


    Lecture 14: 5/1/97

    Class Presentations
    GROUP SPH PROJECT
    SEMESTER PROJECTS