MathMods :: Joint MSc

Sem3 LUH Nonlinear phenomena

leibniz hannover logoApplications  @  LUH  30 ECTS credits

Mathematical models of nonlinear phenomena

The curriculum at the Institute of Applied Mathematics (IfAM) at Leibniz University Hannover is motivated by practical questions from natural sciences, engineering, economics and other fields. Therein, mathematical modelling, theory and numerical methods are addressed. Reliable models for complicated situations are based on natural scientific laws, which can often be described with the help of nonlinear partial differential equations. Consequently, during their semester at LUH, students will be offered rigorous analysis classes, modern numerical analysis, optimization, and courses on application-driven scientific computing. Below you can find a course catalogue listing the subjects taught within MathMods in Hannover. Note: Not all courses will be offered in each semester. 

 

Below you can find information about the courses offered in winter 2025/26

 

  • Numerical methods of partial differential equations with the finite element method [10 credits]

    Numerical methods of partial differential equations with the finite element method

    • ECTS credits 10
    • University Leibniz University Hannover
    • Semester 3
    • Lecturer 1 Sven Beuchler
    • Lecturer 2 Thomas Wick
    • Objectives

       

      This course is devoted to the numerical solution of partial differential equations (PDEs).
      The students will learn how to design numerical algorithms, establish their theoretical properties, and how to realize them in
      implementations.
    • Topics

       

      Recapitulation of characteristic concepts of numerical mathematics
      Brief review of mathematical modeling of differential equations
      Discretization with Finite differences (FD) for elliptic boundary value problems
      Discretization with Finite elements (FEM) for elliptic boundary value problems
      Numerical solution of the discretized problems
      Time-dependent problems: Methods for parabolic and hyperbolic problems
      Numerical methods for nonlinear and coupled problems

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  • Modelling and numerical methods for phase-field fracture in continuum mechanics [5 credits]

    Modelling and numerical methods for phase-field fracture in continuum mechanics

    • ECTS credits 5
    • University Leibniz University Hannover
    • Semester 3
    • Lecturer 1 Thomas Wick
    • Objectives

       

      This course is devoted to numerical modeling of phase-field fracture problems and more
      general numerical modeling of coupled variational inequality systems. Besides a bit recapitulation of continuum mechanics,
      modern nonlinear and linear algorithms are introduced and analyzed.
    • Topics

       

      VI (variational inequality) and propagating interfaces
      Relation to obstacle problems
      Basic from continuum mechanics
      Phase-field fracture systems
      Treating crack irreversiblity: Penalization and primal-dual active set methods
      Nonlinear solution schemes
      Numerical analysis for a simplified problem

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  • Dynamic optimization [5 credits]

    Dynamic optimization

    • ECTS credits 5
    • University Leibniz University Hannover
    • Semester 3
    • Lecturer 1 Marc Steinbach
    • Objectives

       

      This course is devoted to algorithms for optimal control with ODE models.
      The students will implement the multiple shooting method, then formulate
      and solve a concrete problem (e.g., moon landing).
    • Topics

       

      Problem formulation and multiple shooting discretization
      for optimal control and parameter estimation with ODE models,
      algorithms for deterministic and stochastic multistage NLPs,

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  • PDE constrained optimization in engineering and physics [5 credits]

    PDE constrained optimization in engineering and physics

    • ECTS credits 5
    • University Leibniz University Hannover
    • Semester 3
    • Lecturer 1 Sven Beuchler
    • Objectives

       

      The course is devoted to infinite dimensional
      optimization problems which are gouverned by partial
      differential equations.
    • Topics

       

      Linear quadratic optimal control problems
      modelling examples in applications
      existence and uniqueness results
      adjoined state
      discretization and optimization: FEM

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  • Partial differential equations of mathematical biology [5 credits]

    Partial differential equations of mathematical biology

    • ECTS credits 5
    • University Leibniz University Hannover
    • Semester 3
    • Lecturer 1 Johannes Lankeit
    • Objectives

       

      This course gives an introduction to partial differential equations
      arising in mathematical biology and their treatment by mathematical
      analysis.
    • Topics

       

      Diffusion equation, travelling wave solutions, comparison principle for
      parabolic equations, long-term behaviour and blow-up in reaction-diffusion equations,
      energy methods, Keller-Segel system;
      spread of species, reaction-diffusion systems, pattern formation via
      Turing mechanism, chemotaxis

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