In this paper, we develop a fast time-stepping strategy for the Newmark-beta method; the latter is used extensively in structural dynamics. In particular, we speed up the repeated inversion of the linear systems in the Newmark-beta method by implementing and merging four distinct but complementary concepts: (1) voxelization, (2) assembly-free finite element analysis, (3) deflated conjugate gradient, and (4) adaptive local refinement. The resulting assembly-free deflated conjugate gradient (AF-DCG) version of the Newmark-beta is well-suited for large-scale problems, and can be easily ported to multi-core architectures. Numerical experiments demonstrate the efficacy of the proposed method.

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