Vienna
University of Technology
This short course will survey volume-based techniques for solving the Helmholtz equation. We will discuss the classical FEM and show its limitations for large wave numbers k; in particular, quasi-optimality can only be ensured under very stringent conditions on the mesh size h in relation to k. Next, we discuss several methods that are based on using (locally) solutions of the homogeneous Helmholtz equations. These approaches include the partition-of-unity method, the ultraweak formulation of Cessenat & Despres, and Discontinuous Galerkin methods. Concerning problems posed on exterior domain, we will present the use of infinite elements, and a selection of (approximately) absorbing boundary conditions including the perfectly matched layer technique.
Professor Melenk
has an outstanding international reputation for his research in computational mathematics,
especially for his work on hp finite element methods (hp-FEM) and for work on meshfree methods. Indicators of this international
reputation are his many high quality research outputs (two of his papers from
the late nineties have over 240 citations each), his many invitations to speak
at prestigious international meetings, and his recent appointment to a chair in
The lectures will be divided in three topics of roughly equal length:
1. classical FEM for the Helmholtz equation
2. the use of special shape functions for solving teh Helmholtz equation
3. selected topics for exterior domains (infinite elements, PML)
|
12-1 Lecture 1 |
[[Lunch break]] |
|
2-3 Lecture 2 |
[[Coffee Break]] |
|
3:30-5 Problem session |
|
9-10 Lecture 3 |
[[Coffee break]] |
|
10:30-11:30 Lecture 4 |
[[Lunch break]] |
|
2-3:30 Problem session |
|
10-11 Lecture 5 |
[[Coffee break]] |
|
11:30-12:30 Lecture 6 |
[[Lunch break]] |
|
2-4 Problem session |
[[Coffee Break]] |
Accommodation can been arranged in ensuite rooms at Whiteknights Hall, on the university campus. The cost is of GBP 39.95 per night.
In addition to accommodation, breakfast and dinner can be provided at Whiteknights Hall for course residents.
The course is free,
but you should register by sending an e-mail to Mrs. Sue Davis,
s.davis@rdg.ac.uk
Interested participant are strongly encouraged to express their interest informally to the organiser as soon as possible.
Further information available from:
Mrs. Sue Davis
Department of Mathematics
University of Reading
Reading RG6 6AX
Tel. +44 (0)118 3788996
s.davis@rdg.ac.uk.
Page last modified: 7 March, 2008