Hierarchical-ACA DBEM for Anisotropic Three-Dimensional Time-Harmonic Fracture Mechanics

A hierarchical BEM solver for the analysis of three-dimensional anisotropic time-harmonic fracture mechanics problems is presented. A thorough investigation on the relations and interactions between the numerically computed anisotropic fundamental solutions and the algorithm used to approximate the blocks of the hierarchical matrix, namely Adaptive Cross Approximation, is carried out leading to the employed computational strategy. The use of the hierarchical matrices and iterative solvers is proved as an effective technique for speeding up the solution procedure and reducing the required memory storage in time-harmonic three-dimensional anisotropic fracture mechanics problems.