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Astronomy 415 - Fall 2016
``Computational Astrophysics''
cm Instructor

Prof. Massimo Ricotti
Office: PSC 1156
Phone: (301) 405 5097
Office hours: Fri 12:00-1:00pm, 2:00-3:00pm (for this second slot please email me in advance), or by appointment
Class web page:


Jialu Li
Offie: PSC 1248

Class Schedule

Lectures on Tuesday and Thursday from 3:30pm to 4:45pm
Room CSS 2428


This course does not require previous programming experience but if you never learned a compiled programming language, by the end of this course, you will.

I discourage the use of any programming language other than Fortran77, Fortran90, C, C++. The use of Java or python can be discussed. Interpreted programming languages like Matlab, Matematica and IDL are not allowed in this course. The reason is twofold:

The term ``computational astrophysics'' typically refers to running cutting-edge, computationally intensive applications that require high-level efficiency and parallelization. These custom built codes need to run on supercomputers and are typically written in C or Fortran and are parallelized using OpenMP or MPI. Recently, has also become possible to run supercomputer codes on GPU using CUDA or OpenCL languages (we will touch on that).
The course focuses on understanding the mathematical methods involved in writing efficient numerical algorithms. Your goal is to write these algorithms from scratch as a learning process. However, several interpreted programming languages have these algorithms already built in: they work like a ``black boxes'' with an input and an output, thus are not suited for teaching the numerical methods hidden inside the ``black box''.
My ``mother tongue'' is Fortran, but I can also speak C as a second language, and if necessary I can understand some Java or python. Solutions to the homework will be in C.

The level of the class and the topics covered will partially depend on the student's previous familiarity with low-level programming languages. Along the way I may complement the lectures with power point presentations on topics that the class is especially interested in. I will keep the webpage updated and link all the course material there. Laptop computers are allowed in class during the first part of the course.

Course Description

This course will provide students with a basic knowledge of numerical methods commonly used in astrophysics and, more generally, in physics. By the end of the course students should be comfortable working in a Unix environment, compiling and running codes, and employing a variety of visualization techniques to analyze the results. This process will be motivated by concrete examples of modern problems in astrophysics that demand numerical approaches.

As mention above, the material covered will depend on the existing level of computer sophistication among the class participants. However, in broad outline the major course topics will include linear algebra, root finding, least-square fitting, Monte Carlo methods, numerical integration, N-body methods, fluid dynamics, FFTs and time-series analysis.

Recommended Texts

There is no required text for this course. The following recommendations may be helpful to you. Note that much of the course material will follow, Numerical Recipes, which is available online. Most in-class programming examples will be in C, but you are free to chose from any suitable languages for completing the assignments.

Aarseth, S. J. 2003, ``Gravitational -body Simulations: Tools and Algorithms,'' Cambridge Univ. Press.

Hockney, R. W., and J. W. Eastwood 1988, ``Computer Simulation Using Particles,'' Hilger. [Out of print?]

Kernigan, B. W., and D. M. Ritchie 1988, ``The C Programming Language'' (2nd ed.), Prentice-Hall.

Peek, J. D., et al. 1997, ``Learning the Unix Operating System (Nutshell Handbook)'' (4th ed.), O'Reilly.

Prata, S. 1998, ``The Waite Group's C Primer Plus'' (3rd ed.), Howard W. Sams & Co.

Press, W.H. et al. 1992, ``Numerical Recipes in Fortran [or C or C++]'' (2nd ed.), Cambridge Univ Press - visit the website at

Yee, H.C. 1989, ``A class of High-resolution Explicit and Implicit Shock-Capturing Methods'', Tech. Report Lecture Series 1989-04, von Karman Institute of Fluid Dynamics [difficult to find?]

Course Grading

A+ %
A from 96% to 92%
A- from 92% to 88%
B+ from 88% to 84%
B from 84% to 80%
B- from 80% to 76%
C+ from 76% to 72%
C from 72% to 68%
C- from 68% to 64%
D+ from 64% to 60%
D from 60% to 56%
D- from 56% to 52%
F below 52%

There will be no exams in this course. Grades will be determined by homework assignments (6 of them) plus one term paper with the following weights:

Term paper

There will be no curve on the final grades. There may need to be some adjustment to scores depending on the class average; however, any adjustment will be to lower the percentages given above, never to raise them.


Most assignments involve programming exercises. To make evaluating your work easier, you must provide me with a printed solution of the problem and e-mail me a single ``stand-alone'' file containing all your work by the start of class on the day the assignment is due. The file (e.g., a gzip tar archive or a zip file) when uncompressed must produce a folder (named by your last name), containing a suitable formatted response (PDF is best, as Word has compatibility issues especially with embedded figures) to the questions posed in the assignment, along with a description of the remaining contents of the file, including, as needed, instructions on compiling and running any source code. Ideally a Makefile should be provided. Any static graphical output (plots, etc.) should be embedded in the response document. An alternative (and prefered) way to share your homework folder with me is using Dropbox (I will explain in class how it works).

I will compile and run your code with a set of test parameters to ensure correct functionality and error handling. Toward the end of the course, I will also consider your coding style when evaluating your work. Assignments that are late will automatically incur a 10% penalty unless there are extenuating circumstances. The penalty for late assignment will be commensurate to the number of days the homework is late (e.g., % per day). Late assignments must be completed before the solutions are handed in to get any credit.

You may work in groups to discuss programming strategy, but you must submit your own solution to each assignment. Note that, just as for written prose, it is necessary to cite the source of any algorithms you use in completing assignments. This includes Numerical Recipes routines that you use.

Course Policies

The Honor Code

The University of Maryland, College Park has a nationally recognized Code of Academic Integrity, administered by the Student Honor Council. This Code sets standards for academic integrity at Maryland for all undergraduate and graduate students. As a student you are responsible for upholding these standards for this course. It is very important for you to be aware of the consequences of cheating, fabrication, facilitation, and plagiarism. For more information on the Code of Academic Integrity or the Student Honor Council, please visit To further exhibit your commitment to academic integrity, remember to sign the Honor Pledge on all examinations and assignments: "I pledge on my honor that I have not given or received any unauthorized assistance on this examination (assignment)." (NOTE: for the assignments in this course, you may include this statement in your e-mail to me, or the enclosed writeup.)

Course Evaluation

Your participation in the evaluation of courses through CourseEvalUM is a responsibility you hold as a student member of our academic community. Your feedback is confidential and important to the improvement of teaching and learning at the University as well as to the tenure and promotion process. CourseEvalUM will be open for you to complete your evaluations for 2016 Fall semester from early October through December. Please go directly to the website ( to complete your evaluations. By completing all of your evaluations each semester, you will have the privilege of accessing online, at Testudo, the evaluation reports for the thousands of courses for which 70% or more students submitted their evaluations.

Students with Special Needs

Students with a documented disability who wish to discuss academic accommodations should contact me as soon as possible.

Tentative Course Outline

Date Lecture Reading (NRiC)
#1 Aug 30 Introduction to the course and survey -
#2 Sep 01 Computer architecture -
#3 Sep 06 Introduction to UNIX tutorial
#4 Sep 08 Introduction to C 1.1-1.2, tutorial
#5 Sep 13 Examples in C and debugging 1.1-1.2, tutorial
#6 Sep 15 Parallel Computing (CPU and GPU) tutorial
#7 Sep 20 Data representation 1.3
#8 Sep 22 Linear algebra, part 1 (Gauss-Jordan elimination) 2.0-2.3
#9 Sep 27 Linear algebra, part 2 (LU & SVD decomposition) 2.4-2.6
#10 Sep 29 Root finding in 1-D 9.0-9.1, 9.4, 9.6
#11 Oct 04 Root finding in multi-D, and numerical differentiation 5.7
#12 Oct 06 Statistics and the K-S test 14.0-14.3
#13 Oct 11 Least-squares fitting 15.0-15.2, 15.4-15.5
#14 Oct 13 Random numbers and cryptography 7.0-7.2
#15 Oct 18 Numerical integration 7.6, 4.0-4.4, 4.6
#16 Oct 20 Integration of ODEs, part 1 (IVPs) 16.0-16.1
#17 Oct 25 Integration of ODEs, part 2 (leapfrog) -
#18 Oct 27 Integration of ODEs, part 3 (stiff ODEs & 2-pt BVPs) 16.6, 17.0
#19 Nov 01 Integration of ODEs, part 4 (2-pt BVPs) 16.6, 17.0
#20 Nov 03 N-body techniques, part 1 -
#21 Nov 08 N-body techniques, part 2 (PP) -
#22 Nov 10 N-body techniques, part 3 (PM) and 4 (tree) 19.0, 19.4-19.6
#23 Nov 15 Integration of PDEs, part 1 (ell & hyp) 19.0-19.1
#24 Nov 17 Integration of PDEs, part 2 (hyp & par) 19.2
#25 Nov 22 Fluid dynamics, part 1 (eqns) -
- Nov 24 no class (Thanksgiving) -
#26 Nov 29 Fluid dynamics, part 2 (methods) 19.3
#27 Dec 01 Term project presentations -
#28 Dec 06 Term project presentations -
#29 Dec 08 Term project presentations -

Note: check online for up to date Course outline.

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Massimo Ricotti 2016-09-02