For certain problems the use of sophisticated numerical schemes may still
not be sufficient to obtain the desired performance. At this point, one should
consider the development of efficient parallel algorithms that are tailored
for standard high performance cluster systems with either shared or distributed
memory.
Our research in the area of efficient parallel algorithms for scientific computing
includes the following topics:
 Operator Splitting Techniques
For certain problems the use of sophisticated numerical schemes may still
not be enough to obtain the desired performance. At this point, one should
consider the use of high performance cluster systems. In many cases, the
parallelisation of fast sequential algorithms is a very challenging task.
In [1] [2] [3]
we present some parallelisation strategies
for a nonlinear diffusion filter that is based on a highly efficient
additive operator splitting (AOS) scheme. Using the interprocess
communication standard MPI the implemented algorithm showed an excellent
scaling behaviour with speed up factors of up to 209 for 256 processors.
The research on this topic is in cooperation with the Computer Architecture
Group at the University of Heidelberg in Germany.
 Domain Decomposition Methods
Domain decomposition is a frequently used strategy for parallelizing
linear and nonlinear system of equations. Thereby the
original problem is divided in subdomains, for which the problem is solved
locally. From time to time boundaries are updated by solving additional
equation systems that take the global context into consideration.
In [4] [5] [6]
[7] we have developed such domain decomposition
strategies for parallel computation of optic flow fields. The research on
this topic is in cooperation with the Image and Pattern Analysis Group
at the University of Heidelberg in Germany.

A. Bruhn, T. Jakob, M. Fischer, T. Kohlberger, J. Weickert,
U. Brüning, C. Schnörr:
Designing 3D nonlinear diffusion filters for high performance
cluster computing.
In L. Van Gool (Ed.): Pattern Recognition.
Lecture Notes in Computer Science, Vol. 2449, Springer, Berlin,
290297, 2002.

D. Slogsnat, M. Fischer, A. Bruhn, J. Weickert, U. Brüning:
Low level parallelization of nonlinear diffusion filtering algorithms
for cluster computing environments.
In H. Kosch, L. Böszörményi, H. Hellwagner (Eds.):
EuroPar 2003. Parallel Processing.
Lecture Notes in Computer Science, Vol. 2790, Springer, Berlin,
481490, 2003.

A. Bruhn, T. Jakob, M. Fischer, T. Kohlbeger, J. Weickert,
U. Brüning, C. Schnörr:
High performance cluster computing with 3D nonlinear diffusion
filters.
RealTime Imaging, Vol. 10, No. 1, 4151, 2004.
Revised version of
Technical Report No. 87, Department of Mathematics,
Saarland University, Saarbrücken, Germany, 2003.

T. Kohlberger, C. Schnörr, A. Bruhn, J. Weickert:
Domain decomposition for parallel variational optic flow
computation.
In B. Michaelis, G. Krell (Eds.): Pattern Recognition.
Lecture Notes in Computer Science, Vol. 2781, Springer, Berlin,
196202, 2003.

T. Kohlberger, C. Schnörr, A. Bruhn, J. Weickert:
Parallel variational motion estimation by domain decomposition and
cluster computing..
In T. Pajdla, J. Matas (Eds.):
Computer Vision  ECCV 2004.
Lecture Notes in Computer Science, Vol. 3024, Springer, Berlin, 205216, 2004.

T. Kohlberger, C. Schnörr, A. Bruhn, J. Weickert:
Domain Decomposition for Variational Optical Flow Computation.
IEEE Transactions on Image Processing, Vol. 14/8, 11251137, 2005

T. Kohlberger, C. Schnörr, A. Bruhn, J. Weickert:
Domain decomposition for nonlinear problems: a controltheoretic approach.
Technical Report 2005/3, Computer Science Series, University of
Mannheim, April 2005.
