Introduction to Scientific Computing

Semester Hours:

• 2 hours of lectures (WS 2005/06 - ...)
• 2 hours of lectures, 2 hours of tutorials (WS 2001/02 - WS 2004/05)

Audience:

• students in Computational Science and Engineering (CSE) (Int. Master's Program)
• students in Informatik (Hauptstudium, see lectures "Wissenschaftliches Rechnen I+II" in the list "Prüfbare Vorlesungen")
• students in Physik (Hauptstudium)
• students in Mathematik and Technomathematik and other scientific subjects

Classification:

• Master's Program CSE: compulsory course (1st semester, 6 credits)
• Informatik (Diplom/Master): Vertiefende Vorlesung im Bereich theoretische Informatik
• Physik (alle Studienrichtungen): nichtphysikalisches Wahlfach (studienbegleitende DHP-Prüfung)

Curriculum:

From 2001 up to 2005, this course was given in every winter term:

WS 01/02 - WS 02/03 - WS 03/04 - WS 04/05

Starting in winter 2005/2006, the course will be split into "Scientific Computing I" (winter term, 3 credits) and "Scientific Computing II" (summer term, 4 credits).

WS 05/06 - WS 06/07 - WS 07/08 -

The lectures and tutorials are conducted in English.

Requirements:

Vordiplom/Bachelor, or rather the respective lectures in mathematics.

Contents:

This course provides an overview of scientific computing, i. e. of the different tasks to be tackled on the way towards powerful numerical simulations. The entire "pipeline" of simulation is discussed:

• mathematical models:
  derivation, analysis, and classification
• numerical treatment of these models:
  discretization of (partial) differential systems, grid generation
• efficient implementation of numerical algorithms:
  implementation on monoprocessors vs. parallel computers (architectural features, parallel programming, load distribution, parallel numerical algorithms)
• interpretation of numerical results & visualization
• validation

The course is conceived as an introduction to the thriving field of numerical simulation for computer scientists, mathematicians, engineers, or natural scientists without an already strong background in numerical methods.

Scientific Computing II

Scientific Computing II focuses on the efficient solution of (sparse) systems of (mainly linear) equations, as they frequently arise from the discretization of (partial) differential equations. Topics may include:

• Relaxation methods (Jacobi, Gauß-Seidel)
• Multigrid methods
• Conjugate Gradient methods
• Preconditioning
• Nested dissection and domain decomposition