Large-scale Eigenvalue Problems

Richard Lehoucq
Sandia National Laboratories

My presentation discusses the eigenvalue problem in structural dynamics. In particular, my goal will be to discuss recent work on scalable eigensolvers that can be used on large-scale problems arising from 2D and 3D FEM discretizations. After a review of standard approaches, I will introduce component mode synthesis (CMS) methods including an automated multilevel substructuring (AMLS) method. I'll demonstrate that CMS performs a congruence transformation of the underlying symmetric positive definite pencil and represents a projection of the eigenvalue problem onto set of subspaces. My presentation concludes with a discussion and numerical comparison of several scalable eigensolvers on some model 3D problems.

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