文摘
In quasi-dynamic earthquake cycle simulations based on rate and state friction laws, we applied the method of Hierarchical-Matrices (H-matrices) to multiplicative computations of the N ¡Á N slip response function matrix and the slip deficit rate vector, where N is the number of divided cells on the plate surface. H-matrices, which are efficient low-rank compressed representations of dense matrices, enable more rapid arithmetic operations with less memory sizes. In this study, we constructed a friction model of quasi-dynamic earthquake cycles on a flat, dipping, plate interface in a semi-infinite homogeneous elastic medium, and investigated the effectiveness of H-matrices by changing N from 104 to 106. Construction of H-matrices involves several parameters controlling the structure and accuracy of the approximated matrix. With H-matrices using proper values for these parameters to maintain accuracy, except for smaller values of the parameter for suppressing the ranks of the outermost submatrices, the memory size of the matrix was reduced to about O(N). The computational time in the multiplication was also reduced to O(N) for a range of N values less than about 105, and to O(N) ?O(NlogN) for a larger range. Thus, we found that the application of H-matrices greatly reduces the computational time and memory size in earthquake cycle simulations. This advance should enable the realization of large- and multi-scale simulations with a million order cells and the estimation of frictional parameters.
