A log-linear time algorithm for the elastodynamic boundary integral equation method. (1st December 2021)

• Record Type: Journal Article
• Authors: Sato, Dye SK; Ando, Ryosuke
• Is Part Of: Engineering analysis with boundary elements. Volume 133(2021)
• Page Start: 407
• Page End: 450
• Publication Date: 2021-12-01
• Subjects: Elastodynamic analysis -- Time-domain simulations -- H-matrices -- Fast BIEM -- Memory-efficient BIEM; Boundary element methods -- Periodicals; Engineering mathematics -- Periodicals; Équations intégrales de frontière, Méthodes des -- Périodiques; Mathématiques de l'ingénieur -- Périodiques; Boundary element methods; Engineering mathematics; Periodicals; 620.00151
• DOI: 10.1016/j.enganabound.2021.08.026
• Languages: English
• ISSNs: 0955-7997

Abstract

Abstract: 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 ( N log N ) and computation time O ( N M log N ) in our algorithm for a single run with N boundary elements and M time steps. Consequent cost reduction is remarkable, considering the O ( N 2 M ) memory usage and O ( N 2 M 2 ) computational time to run the orthodox time-marching implementation. Numerical experiments verify FDP=H-matrices realize O ( N M / log N ) times smaller memory and computation time with ensuring the accuracy of integral analyses.