PHY 504: Computational Methods in Physics and Astrophysics I

Spring 2024

An introduction to procedural and object-oriented programming in a high-level language such as C++ or modern Fortran with examples and assignments consisting of rudimentary algorithms for problems in physics and astronomy. Students will use the UNIX/Linux operating system to write programs and manage data, and the course will include an introduction to parallel computing and good programming practices such as version control and verification. The course will prepare students for courses in algorithms and methods that assume a knowledge of programming.

Intro & Logistics

• Getting Started
• Topics
• Computation
• Hello, World

The UNIX Shell

• Why Use the Command Line?
• Navigating the Filesystem
• Create Files and Directories
• Redirection and Pipes

Git and Version Control

• Version Control
• Dotfiles and the Mathlab
• A Git Walkthrough
• Git Branches
• Git Remotes
• github
• Pull Requests

Shell Scripting

• Looping on the Command Line
• Shell Scripts
• File Permissions
• Find and Grep

Introduction to Programming

• C++ Textbook
• Computer Hardware
• Software Development Tools
• Structure of a C++ Program
• Helpful C++ Tools / Resources
• Compiling
• Editors
• A First C++ Project

C++ Basics

• C++ Datatypes
• Vectors
• More Vectors
• Example: Matrix
• Aside: Sequence Containers
• Strings
• auto and decltype
• Structures
• Arrays
• References
• Pointers
• Loops and If-Tests
• Maps
• File I/O

Functions

• Functions
• More Functions
• Example: Planetary Orbit
• In Class: 2nd Order Runge-Kutta Orbit
• Lambda Functions
• Example: Sorting Planets

Elements of Software Engineering

• Making the Compiler Do the Work
• Working with Multiple Files
• Makefiles
• In-Class Example: Splitting Up Our Orbit Code

Classes

• Introduction to Classes
• Object-Oriented Design
• In-Class Example: A Simple Grid
• Example: Mathematical Vectors
• In-Class Example: Orbit Integrator Class
• Example: Multidimensional Contiguous Array

Some Random Bits...

• Preview: C++23 mdspan
• Preview: C++23 enumerate and zip
• enum
• Casting
• I/O Manipulators
• Preview: C++23 Print
• Filesystem Library
• Operators
• Floating Point
• Floating Point Exceptions

Testing

• Testing
• Unit Testing
• Continuous integration and github
• Convergence Testing
• Valgrind
• Debugging
• clang-tidy

Digging Deeper into C++ Classes

• Inheritance and Access
• this
• Copy, Assignment, and Destructors
• Compound Assignment Operators
• In-Class Example: Orbit Integrator Compound Operators
• Move Semantics
• Allocating Memory
• Example: A Simple Container

Documenting Code

• HTML + CSS
• Github Pages
• Doxygen
• Sphinx
• Sphinx + Doxygen

Templates

• Templates
• Example: Templated Array
• More On Templates
• constexpr
• Function Objects

Some Numerical Algorithms

• Root Finding
• Monte Carlo Methods
• Adaptive Runge-Kutta
• Poisson Equation and Relaxation

Parallel Programming

• Introduction to Parallel Programming
• OpenMP
• OpenMP Poisson Relaxation
• OpenMP Monte Carlo \(\pi\)
• MPI
• MPI Send and Receive
• MPI Linear Advection Equation

Calling C++ from Python

• pybind11
• Passing a NumPy Array into C++
• Vectoring a C++ Function
• Returning an Array to Python

To Be Continued...

• Stuff We Didn’t Cover
• Coming in C++20
• Coming in C++23
• Some C++ programming terms

Homework

• Homework 1
• Homework 2
• Homework 3
• Homework 4
• Homework 5
• Homework 6
• Homework 7

Project

• Final Project