XFEM
Contents
Dates (SS2015)
The lecture has been held in SS 2015 at TU Wien.
Lecturer: Christoph Lehrenfeld
Poster, TISS, organisational notes (updated), lecture notes
Further information: Prof. Dr. Joachim Schöberl
First meeting: Tue, 3. Mar, 15:00 13:30 , Besprechungszimmer 3. Stock (vis a vis SR 101B)
Lecture+Exercise: Thursday 16:00 - 18:30, Besprechungszimmer 3. Stock (vis a vis SR 101B)
Content
In the lecture modern numerical methods for the discretization of interface problems are presented. Partial differential equations the solution of which has (weak) discontinuities across given interfaces require special care for their numerical treatment. The concept of extended finite element methods (XFEM) introduces finite element spaces which provide ansatz functions which are discontinuous across the interface. Based on this approach the XFEM is used for different applications. We will present interface problems arising in two-phase flow applications and discuss their numerical solution. The lecture includes
- the introduction of XFEM,
- the discussion of implementational aspects
- and their numerical analysis.
The students will work on a student project. Presentation of the problem setting and their solution is part of the course.
Student projects
The Trace FEM for PDEs on surfaces
Project report by T.Jawecki, M. Wess
A fictitious domain method for an osmosis problem
Project report by M. Hochsteger, C. Lackner, L. Kogler
Two-phase Stokes with velocity/pressure XFEM
Project report by P. Lederer, C. Pfeiler, C. Wintersteiger
XFEM discretization of a stationary Stefan problem
Project report by A. Rieder, M. Ruggeri , B. Stiftner
Exercise material / Netgen/NGSolve tutorials
Debian packages for Netgen-6.1-dev and NGSolve-6.1-dev
Exercise schedule / content
- Notes on how to get started with the installation of Netgen/NGSolve, html, pdf
- March, 12th - 26th, 2015: Introduction to Netgen/NGSolve:
- April, 16th-23th, 2015: Introduction to Netgen/NGSolve/NGSxfem
- Exercise material: content(tar-ball)
Other sources for learning to deal with Netgen/NGSolve
- Concepts used in NGSolve:lecture notes 'Scientific Computing'(2004/2005)
- Slides by Christoph Lehrenfeld (Introduction to Netgen/NGSolve):
- NGSolve's pde definition (including geometry): presentation (2009)
- Programming with NGSolve:presentation (2009)
- Slides by Jay Gopalakrishnan (advanced usage of NGSolve):
- "NGSolve::Give me your element?": presentation (2015)
- "NGSolve::What's under the hood?": presentation (2015)
- "NGSolve::Come to the edge": presentation (2015)
- "NGSolve::Take the rough with the smooth": presentation (2015)
Lecture material / literature
Organisational notes:
Lecture notes will be created during the semester.
- Lecture notes (last update: June, 4th, 2015), pdf
Further reading (on which the lecture notes are also based):
- Sven Groß, Arnold Reusken, Numerical Methods for Two-Phase incompressible flows, Springer textbook
- Christoph Lehrenfeld, On a Space-Time Extended Finite Element Method for the Solution of a Class of Two-Phase Mass Transport Problems, Ph.D. thesis, RWTH Aachen, 2015, pdf(A4), pdf(A5)