Christian Lessig

Scientific Computing II: Introduction to Dynamical Systems


Fall/Winter 2019, Otto-von-Guericke Universit├Ąt Magdeburg

Details: Vorlesungsverzeichnis

Lecturer: Christian Lessig

Lectures: Tuesdays, 15:00-17:00, G05-300

Tutorials: Thursdays, 15:00-17:00; G29-426


Content: The course provides the fundamentals to describe the time evolution of ordinary and partial differential equations, e.g. time integrators, the finite element method, and spectral methods.

News


Lectures


Week 1:

Recap linear algebra; dual spaces, dual bases and Riesz representation theorem

Week 2:

Motivation: description of transport by advection equation; analytic solution

Week 3:

Finite difference methods for advection equation

Week 4:

Courant-Friedrichs-Lewy stability condition   Upwind scheme codeCourant-Friedrichs-Lewy's original paper

Week 5:

Consistency, stability, and convergence: Lax-Richtmyer theorem; Galerkin projection; spectral methods

Week 6:

Von Neumann stability analysis; Galerkin projection; spectral methods

Week 7:

Finite element method: fundamentals

Week 8:

Wave equation, theory and finite element formulation


Tutorials


Week 1:

Linear algebra recap; implementation of biorthogonal bases

Week 2:

Finite dimensional function spaces and L_2 inner product

Week 3:

[holiday]

Week 4:

Implicit time stepping schemes   Skeleton code

Week 5:

CFL condition and order for Lax-Richtmyer scheme

Week 6:

[no tutorial]

Week 7:

Von Neumann stability analysis; finite element method

Week 8:

Triangular finite elements


Assignments


Assignment 1:

TaskSkeleton code

Assignment 2:

TaskSkeleton code


Software


We will be working with python and the Numpy library in this course. On Linux you can install it using your package manager. On other operating systems it is convenient to use the Anaconda distribution which contains all necessary packages. An introduction to python and Numpy can be found here.

Literature