Algebraic Multigrid and Multilevel Methods for Vector-Field Problems

Project runtime: 01.02.2007 - 31.01.2010

Project Leader:
Dr.	Johannes Kraus	Direct Field Problems	+43 (0)732 2468 5221	johannes.kraus@oeaw.ac.at

This project is concerned with Algebraic Multigrid (AMG) methods for the solution of large-scale systems of linear algebraic equations arising from finite element (FE) discretization of (systems of) elliptic partial differential equations (PDEs). In particular, we address differential operators with a large (near) nullspace.

Our general objectives are the design, analysis and implementation of new AMG and Algebraic Multilevel (AML) preconditioners that enable an efficient solution of direct field problems in this category: the main emphasis is on problems arising from the discretization of Maxwell's equations, solid and structural mechanical problems with bad parameters, and problems arising in computational fluid dynamics.

The research plan comprises the following components:

1. Investigation of element-based AMG and AML methods regarding non-conforming FE and Discontinuous Galerkin (DG) discretizations.
2. Development of element-, face-, and edge-based strategies for the generation of adequate coarse-grid problems.
3. AMG for non-symmetric and indefinite matrices: Application to (scalar) convection-diffusion, Stokes, and Oseen equations.
4. AMG for non-M matrices: Application to Maxwell's equations and elasticity problems.
5. Implementation of algorithms: Development of a linear solver package (in C/C++).

The main purpose of this project is to contribute in filling the gap between symmetric and positive definite (SPD) M-matrices and general SPD matrices, and, what is even more challenging, between general SPD matrices and non-symmetric and/or indefinite matrices. Besides the investigation of new classes of linear solvers it is also planned to develop a powerful tool kit that can be integrated in other research and commercial software packages as an essential part of the solver kernel.

Project Abstract at FWF

Keywords:

• Algebraic Multigrid
• Multilevel Methods
• Partial Differential Equations
• Finite Element discretization
• Preconditioning
• Linear Solvers

Georgiev, I., Kraus, J., Margenov, S., Multilevel preconditioning of rotated trilinear non-conforming finite element problems, submitted for publication in Springer LNCS, 2007.

---

The Institute is named after the famous Austrian mathematician Johann Radon (1887-1956)

Medieninhaber:
Österreichische Akademie der Wissenschaften
Juristische Person öffentlichen Rechts (BGBl 569/1921 idF BGBl I 130/2003)
Dr. Ignaz Seipel-Platz 2, 1010 Wien
Diese Website dient zur Information über die wissenschaftlichen Aktivitäten der Österreichischen Akademie der Wissenschaften und setzt somit den gesetzlichen Auftrag um, die Wissenschaft in jeder Hinsicht zu fördern.

This RICAM page was made with 100% valid HTML & CSS - Send comments to Webmaster
Today's date and time is 02/09/12 - 19:35 CET and this file ( /projects/AMG_AML/index.html ) was last modified on 05/04/07 - 18:19 CEST