Course Title

Numerical Linear Algebra for High-Performance Computers

Course Code

SDS 421

Course Type

Elective

Level

Master’s

Year / Semester

2^nd Semester

Instructor’s Name

Prof. Vangelis Harmandaris

ECTS

Lectures / week

2

Laboratories / week

1

Course Purpose and Objectives

The aim of the course is to introduce students to tools and algorithms drawn from numerical linear algebra that are used for solving large-scale sparse linear systems of equations. This arsenal of tools lies at the backbone of several key applications in simulation and data science, ranging from computational physics and engineering, to machine learning and network analysis, to name a few.

Learning Outcomes

By the end of the course, students will be able to produce computer codes for solving large-scale linear systems on HPC machines, leveraging iterative algorithms and domain decomposition techniques, as well as analyse and critically assess the performance of the methodologies used.

Prerequisites

Undergraduate-level courses in linear algebra and calculus.

Course Content

The topics to be covered include in a weekly basis:

Week 1: Review of basic elements in numerical linear algebra highlighting the challenges of solving large-scale linear systems with direct methods;

Week 2: Introduction to iterative solvers and spectral methods for sparse matrices;

Week 3: Relaxation schemes;

Week 4: Krylov subspace methods (e.g. Laczos, Arnoldi, conjugate gradient);

Week 5: The GMRES algorithms;

Week 6: Preconditioners for iterative solvers;

Week 7: Introduction to multigrid schemes.

Teaching Methodology

A combination of lectures and hands-on lab session covering both the theoretical and implementation aspects of the material.

Bibliography

Jack J. Dongarra, Iain S. Duff, Danny C. Sorensen, and Henk A. van der Vorst, “Numerical Linear Algebra for High-Performance Computers”, SIAM 1998.

Assessment

Combination of coursework and a final project that includes a report and a presentation

Language

English