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 the notions of Linux/Unix that are required for using high-performance calculators.
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).
Notions of Linux/Unix and initiation to the use of a high-performance computing (HPC) cluster.
Techniques of Parallel Programming
General notions of parallelism
Parallelization using OpenMP
Parallelization using MPI
Parallelization with job arrays
Parallelization on a GPU with OpenCC.
Finite-Difference Methods
Numerical derivatives
Electrostatics
Schrödinger's equation
Numerical stability.
WARNING : this course is meant for students with very good programming skills in Fortran 90.
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
There is a syllabus for the Finite Differences methods.
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. 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 the band structure calculation with OpenMP. Introduction to Linux/Unix and to the use of a high-performance computer.
The theory will be presented using a videoprojector. The exercises will be done on either a personnal computer or in a computer room.
A written exam in Q1 will evaluate the theoretical part of the course (demonstrations, 6 points). An oral exam in Q2 will evaluate the work achieved during the practical sessions. The student will have to show that he acquired the different techniques presented in the course. He will present his solutions for the exercises that come with this course. He must also be able to answer theoretical questions related to the course.
| Training | Study programme | Block | Credits | Mandatory |
|---|---|---|---|---|
| Master in Physics | Finalité spécialisée en physique du vivant | 1 | 3 | No |
| Master in Physics | Finalité approfondie | 1 | 3 | No |
| Master in Physics | Standard | 1 | 3 | No |
| Master in Physics | Finalité didactique | 1 | 3 | No |
| Master in Physics | Finalité spécialisée en physique et data | 1 | 3 | No |
| Master in Physics | Finalité spécialisée en physique du vivant | 2 | 3 | No |
| Master in Physics | Finalité approfondie | 2 | 3 | No |
| Master in Physics | Finalité didactique | 2 | 3 | No |
| Master in Physics | Finalité spécialisée en physique et data | 2 | 3 | No |