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Welcome to Techniques of High-Performance Computing

High-Performance Computing with Python

What is High-Performance Computing?
Languages for High-Performance Computing
Python HPC Tools
Memory layout and Numpy arrays
Parallel Computing Principles in Python
Working with Numba
SIMD Autovectorization in Numba
A Numexpr example
An Introduction to GPU Computing
A tour of CUDA
Numba Cuda in Practice
GPU accelerated evaluation of particle sums

Sparse Linear Algebra

The need for sparse linear algebra - A PDE example
Sparse Matrix data structures
An introduction to sparse linear system solvers
Iterative Solvers 1 - Krylov subspaces, Arnoldi Iteration and the Full Orthogonalisation Method
Iterative Solvers 2 - From FOM to GMRES
Iterative Solvers 3 - The Conjugate Gradient Method
Iterative Solvers 4 - Preconditioning
Sparse Direct Solvers
Using petsc4py for sparse linear systems
Multigrid Methods

Time-Dependent Problems

Simple time-stepping
Discretising the wave equation

Conclusions

Further topics

Late Summmer Assessments

LSA Assignment 1 - Matrix-matrix multiplication
LSA Assignment 2 - GPU Accelerated solution of Poisson problems
LSA Assignment 3 - Sparse matrices
LSA Assignment 4 - Time-dependent problems

Additional notes from 2022

Matrices and simultaneous equations
Python classes

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By Timo Betcke & Matthew Scroggs

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