Caltech's Zwicky Compute Cluster

Computational Astrophysics

Caltech Astrophysics Course Ay 190, Winter Term 2010/2011

Check out the Ay190 Blog!

Instructors: Christian Ott and Andrew Benson


Ay 190, Computational Astrophysics, is a course for graduate students and advanced undergraduates in Astronomy, Physics, Applied Physics, and Geophysics and Planetary Sciences.

Computational modeling is the new frontier of problem solving in astrophysics: For many of the complex heavenly phenomena awaiting understanding, analytical/perturbative techniques have reached their limits and progress can be made only by numerical model building and by contrasting model predictions with observations.

The list of problems that must be addressed with computational models is long and includes (but is by no means limited to!) structure formation and the co-evolution of black holes and galaxies, the chemical evolution of the universe, star formation, stellar evolution, stellar collapse and core-collapse supernove, thermonuclear supernovae, thermonuclear explosions on neutron stars, the coalescence and merger of compact binary systems, common-envelope evolution, stellar dynamics in galaxies and globular clusters, and so on...

The goal of this course is to introduce the basic techniques of numerical and computational modeling and their application to astrophysical systems.

Location:Cahill 219
Days, time, duration: Monday 4:00-5:30pm and Thursday 10:00-11:30am
First class meeting:01/06/2010
Impact:3 hours of lecture per week, ~6 hours of nominal preparation/homework per week.
Prerequisites:For grads: Knowledge of any programming language.
For undergrads: Ph106, Ph20-22, Ay101, Ay21, Ay20
Credit:This class can be counted as credit towards the math physics advanced requirement and the physics masters degree requirements. Undergraduates can apply this course to their advanced physics electives.

List of course topics:
Basic Numerical Analysis Ordinary Differential Equations
Numerical Differentiation Numerical Integration
Linear Systems of Equations Partial Differential Equations
Root Finding Fitting and Data Analysis
Grid-Based Fluid Dynamics (HD/MHD)
Smooth Particle Hydrodynamics
N-Body Algorithms Basic Radiative Transfer
Monte Carlo Methods and more ...

Class Format:

We will meet twice a week in a regular classroom setting. Lectures will be blackboard/whiteboard-style with some use of projection. There will be homework excercise sets to be solved -- generally these will be handed out on a weekly basis, but more comprehensive excercises/projects may span multiple weeks. There will not be a final exam -- rather, there will be an individual term project to be carried out by each participant.

Books and Class Materials:

Unfortunately, there is no textbook for computational astrophysics. The lectures will be based on the instructors' own notes that will be made available here after each lecture.

Class Materials Available on the Ay190 materials webpage (requires username/password).

We recommend the following books and lecture notes as additional reading (list to be expanded):

Press et al.: Numerical Recipies Pang: Computational Physics Bowers and Wilson: Numerical Modeling in Applied Physics and Astrophysics
Ueberhuber: Numerical Computation (1 and 2) Leveque: Finite Difference Methods for Ordinary and Partial Differential Equations Bodenheimer: Numerical Methods in Astrophysics

Software Tools:

Class/homework will be primarily computational and will involve writing code, plotting up results and presenting them in typeset documents. Students may use any combination of programming languages, plotting packages, and typesetting software. However, we strongly encourage the following computational setup:
Operating System: Linux (e.g. Ubuntu, Fedora, Debian) or MacOS X
Programming Language: Python
Plotting Package: matplotlib
Typesetting Package: LaTeX
At the beginning of the term, we will hold a number of help sessions in the evenings in which the instructors and/or grad students Evan O'Connor and Jeff Kaplan will help class participants install these software packages and get up to speed with them.

Preliminary Syllabus:

01/06Introduction and Overview, Numerical Methods Basics Ott and Benson
01/10Numerical Methods I -- Interpolation Ott
01/13Numerical Methods II -- Integration; ODEs Ott
01/17Numerical Methods III -- Basic PDEs Ott
01/20Numerical Methods IV -- Linear/Non-linear Systems Ott
01/24Fitting & Analysis Ott
01/27Monte Carlo Ott
01/31Computational Fluid Dynamics: Basics Ott
02/03Grid-Based Computational Fluid Dynamics I Ott
02/07N-Body & SPHBarnes & Hut 1986Benson
02/10N-Body & SPH Benson
02/14N-Body & SPHSpringel 2010Benson
02/17N-Body & SPH Benson
02/21Grid-Based Computational Fluid Dynamics II -- Applications Ott
02/24Magnetohydrodynamics Ott
02/28Radiation Transport Basics Ott
03/03Radiation Transport Applications Ott
03/07Radiation Transport Applications Ott
03/10Special Topic Ott

Last change: 11/19/2010, CDO