Learning outcomes
The student will learn advanced programming techniques and the use in command lines of free and performant tools. The main objective of this course is parallel programming (OpenMP, MPI and OpenACC libraries). The student will apply finite-difference techniques for the resolution of typical problems in physics. The student will also get notions of Unix as required for the use of a computer cluster.
Content
Working with command lines. Installation of a complete work environment with free and performant tools. Advanced use of the gfortran compiler (compilation using a Makefile, optimization, debugger, profiling). Techniques of Parallel Programming : 1. General notions of parallelism 2. Parallelization using OpenMP 3. Parallelization using MPI 4. Parallelization with job arrays 5. Parallelization on a GPU with OpenCC. Finite-Difference Methods : 1. Numerical derivatives 2. Electrostatics 3. Schrödinger's equation 4. Numerical stability. Introduction to Evolutionary Computing (Machine Learning). Notions of Unix and initiation to the use of a computer cluster.
WARNING : this course is meant for students with very good programming skills in Fortran 90.
Table of contents
1. Advanced use of the gfortran compiler
working with command lines
Makefile, debugger, profiling
Introduction to the cluster (Linux, ifort compiler)
Fortran 90 : advanced notions
2. Finite Differences methods
Numerical Derivatives
Electrostatics
Equation of Laplace, equation of Poisson
Direct approach by the resolution of a system of linear equations
Method of Jacobi, method of Gauss-Seidel, method of over-relaxation
Equation of Schrödinger
Eigensystem approach
Eigenstates of a potential
Band structures
Continued fractions
Eigenstates of a potential
Transmission through a potential barrier
Time-dependent Schrödinger's equation
Numerical stability of a discretization scheme
3. General notions of parallelism
concepts of cpu time, wallclock time, speedup, efficiency, load balancing, multithreading
Amdahl's law, how to parallelize
automatic parallelization with ifort
4. Parallelization with OpenMP
OpenMP with gfortran and ifort
scripts to use on the cluster
presentation of the OpenMP library
5. Parallelization with MPI
MPI with gfortran and PGI
scripts to use on the cluster
presentation of the MPI library
6. Use of jobarrays on the cluster
Execution of parallel scripts on Windows
7. Parallelization with OpenACC (GPU)
PGI Compiler & PGI Profiler
scripts to use on the cluster
presentation of the OpenACC library
comparison between different methods of the parallelization of Poisson's equation
8. Introduction to Evolutionary Computing
Genetic Algorithms, Genetic Programming, Artificial Intelligence
Demonstration : Supervised Learning on MNIST with TensorFlow
Demonstration : Deep Reinforcement Learning (Deep Q-Learning) on Breakout
There is a syllabus for the Finite Differences methods.
Exercises description
Use in command lines of the gfortran compiler. Compilation using a Makefile. Installation of a complete work environment. Compilation of a program that uses OpenMP. Numerical resolution of Poisson's equation. Calculation of the bound states of an harmonic potential. Calculation of the band structure of a periodic potential. Calculation of electronic scattering through a potential barrier. Parallelization of one of these problems with OpenMP or OpenACC. Introduction to Unix and to the use of a computer cluster.