Iterative 3D BEM solver on complex faults geometry using angular dislocation approach in heterogeneous, isotropic elastic whole or half-space

Abstract

Based on the analytical solution of the induced displacement caused by a 3D angular dislocation, it is possible to construct closed polygonal loops with constant burgerss vector, from which the stress is derived using linear elasticity in homogeneous, isotropic whole- or half-space. In this BEM code, each fault is discretized as a triangulated mesh, where mixed boundary conditions are prescribed. Incorporate material heterogeneity is done by using triangulated interfaces made of dual-elements with prescribed continuity and equilibrium conditions. Each interface and fault can therefore have a complex 3D geometry with no gaps or overlaps between elements. We use an iterative solver where the system of equations is decomposed at the element level, allowing a simple formulation of the boundary conditions for elements making a fault, and continuity/equilibrium conditions at dual-elements making an interface. It is shown that strict diagonal dominance can be achieved only if continuity and equilibrium conditions, for a given dual-element, are solved simultaneously. Using a Gauss-Seidel-like method, we consequently reduce the complexity while automatically taking care of the sparsity of the system. Moreover, using a Jacobi-like solver, we show that the resolution of the system can simply be parallelized on multi-core processors. Some comparisons with a 2D analytical solution and a 2D BEM code are presented.