21st GAMM-Seminar Leipzig on
Robust Fast Solvers

Max-Planck-Institute for Mathematics in the Sciences
Inselstr. 22-26, D-04103 [O->]Leipzig
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  21st GAMM-Seminar
January, 26th-28th, 2005
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  Abstract Jeffrey Ovall, Thu, 16.30-17.15 Previous Contents Next  
  Dual Functions for Parallel Adaptive Methods
Jeffrey Ovall (MPI Leipzig)

In 2000 Bank and Holst proposed a new paradigm for parallel adaptive meshing algorithms [SIAM J. Sci. Comp., 22 (4), 2000; SIAM Review, 45 (2), 2003]. The load balancing problem, which is problematic for many algorithms, is addressed by solving a small elliptic problem on a single processor (or independantly on all processors), and using a posteriori error estimates to partition the domain. Each processor then independently performs several iterations of solve-estimate-refine on the entire problem until a target number of vertices is reached, with the error estimates outside of its assigned subdomain artificially damped by 10-6. At the end of this second stage a global conforming mesh is formed from the fine contributions from each processor, and a final global parallel iterative solve done on this mesh with the initial guess build from the fine solutions on each processor. The ability of the second stage to provide an adequate setup for the final global solve is strained somewhat by the presence of singularities or other phenomena which have an unusually strong influence on global behavior. We propose a different error estimate weighting scheme which is based on the solution of an appropriate dual problem, and which better takes into account global influences on local behavior.

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Last updated:
28.01.2005 Impressum
Concept, Design and Realisation
[O->]Jens Burmeister (Uni Kiel), Kai Helms (MPI Leipzig)
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