Project P14953 - Institute of Computational Mathematics

Robust Algebraic Multigrid Methods and their Parallelization

Supported by the Austrian Science Foundation - " Fond zur Förderung der wissenschaftlichen Forschung (FWF) " under the grant P14953 "Robust Algebraic Multigrid Methods and their Parallelization" (October 1, 2001 - September 30, 2005)

Abstract

The aim of this project is the development and construction of Algebraic MultiGrid (AMG) methods. AMG methods try to mimic geometric multigrid methods just by knowing single grid information but retaining the optimality of the method. Since the construction of an universal AMG method for all arising situations in practice is an unrealistic dream, we will assemble efficient and robust solvers for special classes of matrices such as large scale systems arising from the (FEM, FDM, FIT, BEM) discretization of:

Anisotropic Potential Equation
Maxwell's Equations
Stokes / Navier-Stokes Equations

Navier-Stokes-flow past a half-opened valve.
(Geometry provided by AVL List GmbH)

Maxwell equations
quarter of a magnetic valve

Moreover, parallelization of AMG method is an important task, because it is the main source for a further enhancement of efficiency in real life applications.

Objectives

efficient solution of positive definite and indefinite equations with AMG
parallelization of AMG
software development
real life application

Results

Publications

Conferences and Talks

Software

AMuSE Algebraic Multigrid for Stokes type Equations
PEBBLES Parallel Element Based grey Box Linear Equation Solver

Special CVS Issue

On Fast Boundary Element Methods in Industrial Applications

Cooperations

Institute of Sensor Technology , Erlangen, Germany (Prof. R. Lerch, Dr. M. Kaltenbacher)
Max Planck Institute for Mathematics in the Sciences , Leipzig, Germany (C. Wolters)
Institute of General Electrical Engineering , Rostock, Germany (Prof. U. van Rienen, Dr. U. Schreiber, Dr. G. Pöplau)
Working Group MAGNET, Vienna University of Technology, Vienna, Austria (Dr. T. Schrefl)
Institute of Applied Mathematics and Numerical Simulation, Stuttgart, Germany (PD Dr. Olaf Steinbach)
START-Project "3D hp-Finite Elements: Fast Solvers and Adaptivity", Linz (Dr. J. Schoeberl, ...)
Radon Institute for Computational and Applied Mathematics (RICAM), Linz (Dr. J. Kraus)

AMG-Links

Prof. Achi Brandt, Weizmann Institute, Israel
Center for Applied Scientific Computing (CASC) , Lawrence Livermore National Labs, R. Falgout, J. Jones, P. Vassilevski, V.E. Henson, ....
Dr. Klaus Stüben, Bonn, Germany
Center for Computational Mathematics , Prof. J. Mandel
University of Colorado at Boulder, Dept. of Applied Mathematics, M. Brezina, J. Ruge
Dr. Christian Wagner
Dr. Matthias Bollhöfer , TU Berlin
Prof. Michael Griebel, University of Bonn
MGNet

Diploma Theses

The diploma theses topic can be combined with the "Project Seminar" held every spring term at the Institute ofComputational Mathematics. Additionally the diploma theses consists in a special application from industry. The proposed topics should be seen as a collection of possible subjects. Other suggestions are warmely welcome.

Algebraic Multigrid Methods for Navier-Stokes Equations
Algebraic Multigrid Methods for Convection Diffusion Equations
Algebraic Multigrid Methods on Parallel Computers
Algebraic Multigrid Methods in Structural Mechanics
Algebraic Multigrid Methods for Maxwell's Equations
Algebraic Multigrid Methods for Helmholtz Equations
Complex versions of the above topics

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