# Large-scale problems in Science and Technology:

Methods and Algorithms, 5hp

## General aims of the course

The modeling, analysis, and optimization of many phenomena in science and technology increasingly involve computational methods and algorithms that need to be developed to perform well for large problems. The aim of this course is to present an overview of computational techniques that are commonly applied for large-scale computational problems. The course modules are devoted to the solution of large sparse linear systems, large-scale discrete problems modeled by means of cellular automata and graphs, combinatorial optimization, and computational methods suitable for field problems. The focus is on modeling, algorithms, and implementation issues related to such problems.

The participants will obtain an overview of a selection of important methods and modeling techniques. This knowledge will in turn act as a guideline when addressing large-scale problems in the participant’s own research.

## Course contents

The course is partitioned into four modules:

- Large sparse linear systems (direct and iterative methods)
- Large-scale discrete problems modeled by means of graphs (cellular automata and graph analysis)
- Numerical methods for combinatorial optimization problems
- Numerical methods for models of field problems (finite differences, finite volumes, finite elements)

## Learning outcomes

After completing the course you should be able to:

- …explain the underlying theory and limitations of fundamental methods

for solving large sparse systems of linear equations. - …explain the impact of preconditioning on the convergence of iterative methods.
- …explain how certain problems can be modeled discretely by means of

graphs and solve basic graph analysis problems. - …explain basic properties and now how to apply basic versions of the finite difference,

finite volume, or finite element methods for solving common field problems

governing for instance diffusion or wave propagation. - …use standard software packages to solve such problems.

The examination is performed using a number of homework assignments.

## Prerequisites

Scientific Computing I (SeSE course) or equivalent.

Course schedule

- Week 23 (preparatory work at home)
- Week 24 (lectures in Umeå)
- Week 25 (homework)

## Registration

Please register here before **May 12**

## Contact

**Martin Berggren:** martin.berggren@cs.umu.se