Simulation Methods for Distributed SystemsMichel Make
The lecture deals with the mathematical basics of the finite element method from the perspective of a mechanical engineer. It is complemented by a programming exercise.
Lecture: Prof. Dr.-Ing. Stefanie Elgeti
Laboratory exercises: Fabian Key, M.Sc.
The course is a continuation of the lecture “Simulation Methods in Mechanical Engineering”. It deepens the understanding already gained in the area of distributed systems. The topic of finite elements receives special attention. The course treats further differential equations which are relevant in mechanical engineering. The special aspects of each governing equation are discussed. The topics of geometry definition and adaptation, free-surface problems and non-standard interpolation function spaces are covered. Additional time discretization techniques are introduced. In addition, efficient solution techniques for the large linear systems of equations arising from the discretization of distributed systems are presented.
The module consists of a lecture and a programming exercise with 2 SWS each, and carries 6 ECTS points.
- introduction to differential equations
- weak solution of a differential equation
- finite element method
- time discretization methods
- iterative solvers
- H. Elman, D. Silvester, A. Wathen, Finite Elements and Fast Iterative Solvers with Applications in Incompressible Fluid Dynamics , Oxford University Press
- A. Quarteroni, Numerical Models for Differential Problems , Springer
- A. Quarteroni, F. Saleri, P. Gervasio, Scientific Computing with MATLAB and Octave , Springer
Bonus points will be awarded on the basis of the programming exercise. Oral exams take place on several dates after the end of the lecture phase.