The primary computational bottle-neck in implicit structural dynamics is the repeated inversion of the underlying stiffness matrix. In this paper, a fast inversion technique is proposed by merging four distinct but complementary concepts: (1) voxelization with adaptive local refinement, (2) assembly-free (a.k.a. matrix-free or element-by-element) finite element analysis (FEA), (3) assembly-free deflated conjugate gradient (AF-DCG), and (4) multicore parallelization. In particular, we apply these concepts to the well-known Newmark-beta method, and the resulting AF-DCG is well-suited for large-scale problems. It can be easily ported to many-core central processing unit (CPU) and multicore graphics-programmable unit (GPU) architectures, as demonstrated through numerical experiments.
A Deflated Assembly Free Approach to Large-Scale Implicit Structural Dynamics
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received June 27, 2014; final manuscript received November 12, 2014; published online April 9, 2015. Assoc. Editor: José L. Escalona.
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Mirzendehdel, A. M., and Suresh, K. (November 1, 2015). "A Deflated Assembly Free Approach to Large-Scale Implicit Structural Dynamics." ASME. J. Comput. Nonlinear Dynam. November 2015; 10(6): 061015. https://doi.org/10.1115/1.4029110
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