Iterative Solution of Large Scale Systems in Scientific Computing
A core problem in Scientific Computing is the solution of nonlinear and linear systems. These arise in the solution of boundary value problems, stiff ODEs and in optimization. Particular difficulties appear when the systems are large, meaning millions of unknowns. This is often the case when discretizing partial differential equations which model important phenomenas in science and technology. Due to the size of the systems they may only be solved using iterative methods.
The aim of this course is to teach modern methods for the solution of such systems.
The course is a direct follow up of the course FMNN10 Numerical Methods for Differential Equations, and expands the student's toolbox for calculating approximative solutions of partial differential equations.
Assignments: These are given out weekly and are mandatory, but are not taken into account for your grade.
Projects: There is one final project for which you need to hand in a project report.
Grade: The project report gives 50% of the grade, the oral exam based on the project report the other half.
Where do large scale linear and nonlinear systems arise in Scientific Computing? Speed of convergence; Multigrid methods in one and two dimensions; Multigrid methods for nonstandard equations and for nonlinear systems; Termination criteria; Fixed Point methods and convergence theory; Newton's method, its convergence theory and its problems; Inexact Newton's method and its convergence theory; Methods of Newton type and convergence theory; Linear systems; Krylov subspace methods and GMRES; Preconditioning GMRES; Jacobian-free Newton-Krylov methods