A log-linear time algorithm for the elastodynamic boundary integral equation method

We present a fast and memory-efficient algorithm for transient space–time-domain elastodynamic boundary-integral analysis. Associated data-sparse approximations and operations are named fast domain partitioning hierarchical matrices (FDP=H-matrices). The fast domain partitioning method (the FDPM) so...

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Bibliographic Details
Published in:Engineering analysis with boundary elements 2021-12, Vol.133, p.407-450
Main Authors: Sato, Dye SK, Ando, Ryosuke
Format: Article
Language:English
Subjects:
Elastodynamic analysis
Fast BIEM
H-matrices
Memory-efficient BIEM
Time-domain simulations
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Summary:We present a fast and memory-efficient algorithm for transient space–time-domain elastodynamic boundary-integral analysis. Associated data-sparse approximations and operations are named fast domain partitioning hierarchical matrices (FDP=H-matrices). The fast domain partitioning method (the FDPM) solves a known problem of hierarchical matrices (H-matrices) in compressing discretized elastodynamic kernel functions. A novel set of plane-wave approximations unites the FDPM and H-matrices in an accurate analytic manner. Memory usage is O(NlogN) and computation time O(NMlogN) in our algorithm for a single run with N boundary elements and M time steps. Consequent cost reduction is remarkable, considering the O(N2M) memory usage and O(N2M2) computational time to run the orthodox time-marching implementation. Numerical experiments verify FDP=H-matrices realize O(NM/logN) times smaller memory and computation time with ensuring the accuracy of integral analyses.
ISSN:0955-7997
1873-197X
DOI:10.1016/j.enganabound.2021.08.026