Third-Cycle Courses

Faculty of Engineering | Lund University

Details for the Course Syllabus for Course FMN020F valid from Spring 2016

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  • 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.
  • 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

Knowledge and Understanding
  • For a passing grade the doctoral student must
  • understand basic iterative methods for linear and nonlinear equations, and understand their mathematical differences

    understand the framwork of Jacobian-free Newton-Krylov methods

    understand multigrid methods for model problems.
Competences and Skills
  • For a passing grade the doctoral student must
  • be able to implement an inexact Jacobian-free Newton-Krylov method

    be able to implement a multigrid method for model problems

    be able to apply basic iterative solvers in a computer program.
Judgement and Approach
  • For a passing grade the doctoral student must
  • be able to decide, given information about a nonlinear or linear system, which solver to use and which not to.
Types of Instruction
  • Lectures
  • Exercises
  • Project
Examination Formats
  • Oral exam
  • Written report
  • Failed, pass
Admission Requirements
Assumed Prior Knowledge
  • FMNN10 Numerical Methods for Differential Equations.
Selection Criteria
  • Kelley, C. T.: Iterative Methods for Linear and Nonlinear Equations. SIAM, 1995. ISBN 9780898713527.
    Wesseling, P.: An Introduction to Multigrid Methods. R T Edwards, 2004. ISBN 9781930217089.
Further Information
Course code
  • FMN020F
Administrative Information
  •  -11-13
  • FN1/AndersGustafsson

All Published Course Occasions for the Course Syllabus

1 course occasion.

Start Date End Date Published
2016‑01‑18 (approximate) 2016‑03‑16

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