Iterative 3D BEM Solver On Complex Faults
Geometry Using Angular Dislocation
Approach In Heterogeneous, Isotropic
Elastic Whole Or Half-space
Author(s)
F. Maerten & L. Maerten
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
Burgers’s vector, from which the stress is derived using linear elasticity in homogeneous,
isotropic whole- or half-space. In this BEMcode, each fault is discretized
as a triangulated mesh, where mixed boundary conditions are prescribed.
Incorporatematerial 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 elementsmaking
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.
Keywords: iterative solver, indirect method, heterogeneity, optimization, complex
3D geometry.
Keywords
iterative solver, indirect method, heterogeneity, optimization, complex
3D geometry.
Related Book
Other papers in this volume
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