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) 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((NM)-M-2) memory usage and O((NM2)-M-2) computational time to run the orthodox time-marching implementation. Numerical experiments verify FDP=H-matrices realize O(NM/log N) times smaller memory and computation time with ensuring the accuracy of integral analyses.