ABSTRACT
We present the theoretical and computational implementation of an original version of the Fast Multipole Method (FMM) for solving large-scale problems in 3D elastostatics based on the indirect boundary integral fictitious formulation. The conventional boundary element method with N collocation nodes, translates into solving a dense and non-symmetric system of equations, with computational complexity O(N2). Additionally, for large models, storing the system’s matrix in random-access memory (RAM) is intractable, requiring storing sections of the matrix in hard disk. This creates an important burden towards computational cost. The FMM is inspired on the intuitive idea of collecting influences (e.g., gravitational, electromagnetic, acoustic, elastic) from close sources into a single source, using approximations with the flavor of a Taylor expansion. We illustrate the power of the method applied in computing 3D elastostatics models for real-world excavations, running within Rocscience modelling software, where important speed-ups were observed for a wide range of models ranging from 100K up to 1M elements.
