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Fande Kong
A multilevel domain decomposition method with a boundary geometry preserving coarse space for elasticity equation

Department of Computer Science
University of Colorado Boulder
Boulder
Colorado 80309-0430
fande.kong@colorado.edu
Xiao-Chuan Cai

Domain decomposition method is a popular approach for solving elasticity equations discretized by the finite element method on 3D unstructured meshes. The method is scalable in term of the number of iterations if appropriate coarse spaces are used. However, it is nontrivial to construct an algorithm that is highly scalable in term of the total compute time, especially when the number of processors is large and the computational domain is complex, because the coarse solver itself is not often scalable and accounts for a large percentage of the total compute time. To fix the issue, a new algorithm is introduced to construct coarse spaces by retaining a set of important boundary vertices and deleting a set of interior vertices such that they preserve the boundary geometry of the fine mesh and use only a small amount of compute time by giving up the solution accuracy in the interior. It turns out that the geometry preserving feature of the coarse space makes the method highly scalable in terms of the number of iterations and the total compute time even when the number of processors is large. The low coarse solution accuracy does not change the final solution accuracy since the coarse solver is only part of the preconditioner. We show numerically that the method is highly scalable for some 3D elasticity problems on a supercomputer with over 10,000 cores.




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Copper Mountain 2014-02-23