Gäller från och med: Spring 2016
Beslutad av: FN1/Anders Gustafsson
Datum för fastställande: 2015-11-13
Avdelning: Numerical Analysis
Kurstyp: Ren forskarutbildningskurs
Undervisningsspråk: English
A core problem in Scientific Computing is the solution of nonlinear and linear systems. These arise in the solution of boundary value problems, stiff ordinary differential equations 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 postgraduate student's toolbox for calculating approximative solutions of partial differential equations.
Kunskap och förståelse
För godkänd kurs skall doktoranden
Färdighet och förmåga
För godkänd kurs skall doktoranden
Värderingsförmåga och förhållningssätt
För godkänd kurs skall doktoranden be able to decide, given information about a nonlinear or linear system, which solver to use and which not to.
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 - the Generalized Minimal RESidual method Preconditioning GMRES Jacobian-free Newton-Krylov methods Multigrid methods in one and two dimensions Multigrid methods for nonstandard equations and for nonlinear systems
Undervisningsformer: Föreläsningar, övningar, projekt
Examinationsformer: Muntlig tentamen, skriftlig rapport
Betygsskala: Underkänd, godkänd
Examinator:
Förutsatta förkunskaper: FMNN10 Numerical Methods for Differential Equations.
Kursansvarig: Gustaf Söderlind <gustaf.soderlind@math.lu.se>
Hemsida: http://www.ctr.maths.lu.se/course/IterSol/