Iterative Nonlinear Solvers for Large Linear Systems of Equations

Abstract

Developing numerical methods for the solution of systems of partial as well as ordinary differential equations one is often faced with the crucial problem that the overall performance of the scheme depends decisively on the efficiency of the incorporated solvers for the internal nonlinear or even linear systems of equations.

The course is design to give a comprehensive overview on modern numerical solution techniques for large linear systems of equations. In order to enable a successive participation for students and researchers from a wide variety of scientific disciplines like civil as well as mechanical enginieering, physicists, mathematicians but even different other research areas, we will start with an introduction of classical iterative methods like Jacobi- and Gauss-Seidel schemes as well as there extension by relaxation. Furthermore, we will focus on different Krylov subspace schemes like CG, GMRES, BICGSTAB and so on. Finally, we will also discuss the important field of preconditioning.

The course includes not only lectures but also practical exercises, where the participants will write their on numerical schemes based on templates given by the lecturer.

Participants are encouraged to bring their own laptop with an operative version of OCTAVE installed. This short course will be taught in the English language.

Andreas Meister CV

Contact: ignacio.muga@pucv.cl

Program

Day 1:

09:00 – 10:30 Lecture: Introduction to Splitting Methods
10:30 – 11:00 Coffee break
11:00 – 12:00 Lecture: Jacobi-, Gauss-Seidel-Method and
relaxation techniques
12:00 – 13:30 Exercise on Splitting Methods
13:30 – 14:30 Lunch break
14:30 – 15:30 Lecture: Method of Conjugate Gradients
15:30 – 16:00 Coffee break
16:00 – 17:30 Exercise on Method of Conjugate Gradients

Day 2:

09:00 – 10:30 Lecture: Principles of Multigrid Methods
10:30 – 11:00 Coffee break
11:00 – 12:30 Lecture: GMRES, BICG, BICGSTAB
12:30 – 13:30 Lunch break
13:30 – 15:00 Exercise on Multigrid and Krylov Subspace Methods
15:00 – 15:30 Coffee break
15:30 – 16:30 Lecture: Preconditioning
16:30 – 17:00 Concluding Discussion