期刊
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
卷 274, 期 -, 页码 19-41出版社
ELSEVIER SCIENCE SA
DOI: 10.1016/j.cma.2014.01.023
关键词
Fast isogeometric solvers; Finite element method; Explicit dynamics; Tensor product; L2 projection; Mass matrix
资金
- King Abdullah University of Science and Technology (KAUST) Center
- Academic Excellence Alliance program award from KAUST's Global Collaborative Research
In finite element analysis, solving time-dependent partial differential equations with explicit time marching schemes requires repeatedly applying the inverse of the mass matrix. For mass matrices that can be expressed as tensor products of lower dimensional matrices, we present a direct method that has linear computational complexity, i.e., O(N), where N is the total number of degrees of freedom in the system. We refer to these matrices as separable matrices. For non-separable mass matrices, we present a preconditioned conjugate gradient method with carefully designed preconditioners as an alternative. We demonstrate that these preconditioners, which are easy to construct and cheap to apply (O(N)), can deliver significant convergence acceleration. The performances of these preconditioners are independent of the polynomial order (p independence) and mesh resolution (h independence) for maximum continuity B-splines, as verified by various numerical tests. (c) 2014 Elsevier B.V. All rights reserved.
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