Matematikcentrum

Lund University

Iterativ lösning av storskaliga system i beräkningsteknik

Kursplan

Beskrivning

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.

Contents

Where do large scale linear and nonlinear systems arise in Scientific Computing? Speed of convergence Termination criteria Fixed Point mehtods 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 Multigrid methods in one and two dimensions Multigrid methods for nonstandard equations and for nonlinear systems

Kommande kursomgångar

Kursinformation

Kurskod LTH:FMNN30
Kurskod NF: NUMN30
Poäng:7,5
Nivå:Avancerad nivå
Språk:Engelska

Förkunskapskrav

CEQ

CEQ - Iterativ lösning av storskaliga system i beräkningsteknik