Fast solvers, analytical construction

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Aim:

Within the Sonderforschungsbereich 393 "Numerical simulation in massively parallel computers" the project A3 (fast solvers, analytical construction) is of very importance. The efficient solution of large scale systems of linear algebraic equations is often absolutely necessary for the numerical tackling of problems having very different background. In the recent time the development of fast parallel solution methods for large systems of mesh equations represents one of the research topics in mathematical physics that became very up to date internationally. Searching for the project A3 we continue the work which was already done in Chemnitz for the fast solution of systems of equations arisen from the finite element discretization of several specific problems in continuum mechanics and computational fluid dynamics. Doing as given, the further development of parallel algorithms handling uniform refined three dimensional discretizations as well as the implementation of parallel solvers using adaptive grids must be analysed and performed.

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Members:

• Prof. D. A. Meyer
• Dr. M. Jung
• Dr. T. Apel
• Dr. G. Globisch
• Dipl.Math. S. Beuchler

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Projects:

• Development of efficient parallizable DD-methods, Multigrid-processes and BPX-like preconditioners for equation systems arising in finite-element-discretization of elliptic boundary value problems in 3D-domains
• Development of efficient solution techniques for problems in domains in which a simple triangulation is not constructable
• Development of DD and Multilevel preconditioners for problems of plates and shells
• Development of efficient processes with bad parameters, maybe elasticity problems with Poisson ratio near 0.5; equations such as ,

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Applications

• simulation of current
• Lamé-equations, elasto-plastic problems
• problems of plates and shells

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Software

SPC-PM PO2D	general 2D-potential problems
SPC-PM EL	elastic problems
SPC-PM EP	elasto-plastic problems
SPC-PM CFD	coupled simulation pf current
SPC-PM Po 3D	general 3D-potential problems
FEMooBEM	coupled FE-/BE-diskretization
SPC-PM2Ad	2D- adaptive solving potential or elasticity problems
	in xy- oder cylindrical coordinates
	(triang./quadr.-meshes - error estimator - possibly hanging nodes)

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H. Rhein, October 1997