09:15 〜 09:30
[STT43-02] FDP-LH行列法による動的破壊シミュレーション高速化
キーワード：境界積分方程式法、動的破壊シミュレーション
Dynamic rupture simulation is essential for understanding the physical mechanism of earthquakes. The elastodynamic boundary integral equation method (BIEM) is often used for its simplicity of applying to the non-palnar faults. In the BIEM, the stress is obtained by the space and time convolution of the slip velocity and integration kernel. Naive algorithm requires the order of the computation O(N2M2) and the amounts of memory O(N2M) , with the number of meshes N, and the time steps M. Therefore, simulation on large fault demands tremendous computational complexity and massive amounts of memory and efficient algorithms are needed.
Ando(2016) suggested Fast Domain Partitioning (FDP) Method which partition causality cone the region where elastic waves affect into P and S wave fronts (Domain Fp, FS), the domain between P and S waves (Domain I), and the domain of the static equilibrium (Domain S). Each domain shows the different nature of kernel and this allows for fast computation.
Sato and Ando(2021) developed a new approximation algorithm called FDP=H-matrices and they acheived computational complexity O(NlogNM) by incorporating H matrices into FDPM with the use of travel-time approximation. They solved 2D elastodynamic wave propagation problems and confirmed its utilities.
In this research, we slightly changed the algorithm of Domain I not to use approximation and applied to 3D dynamic rupture simulation. Furthermore, instead of using H matrices, we adopted Lattice H matrices(Ida 2018) as low-rank approximation methods. Lattice H matrices are constructed by blocks of lattice structures which consist of H matrices as submatrices in order to efficiently use a large number of process. For simplicity, we set the fault plane in parallel and investigated the accuracy of calculation and the spped of the simulation. The results indicate the potential to apply this FDP=LH-matrices method to actual earthquake simulations.
Ando(2016) suggested Fast Domain Partitioning (FDP) Method which partition causality cone the region where elastic waves affect into P and S wave fronts (Domain Fp, FS), the domain between P and S waves (Domain I), and the domain of the static equilibrium (Domain S). Each domain shows the different nature of kernel and this allows for fast computation.
Sato and Ando(2021) developed a new approximation algorithm called FDP=H-matrices and they acheived computational complexity O(NlogNM) by incorporating H matrices into FDPM with the use of travel-time approximation. They solved 2D elastodynamic wave propagation problems and confirmed its utilities.
In this research, we slightly changed the algorithm of Domain I not to use approximation and applied to 3D dynamic rupture simulation. Furthermore, instead of using H matrices, we adopted Lattice H matrices(Ida 2018) as low-rank approximation methods. Lattice H matrices are constructed by blocks of lattice structures which consist of H matrices as submatrices in order to efficiently use a large number of process. For simplicity, we set the fault plane in parallel and investigated the accuracy of calculation and the spped of the simulation. The results indicate the potential to apply this FDP=LH-matrices method to actual earthquake simulations.