Abstract
Because of the non-local nature of the integral kernels at play, the discretization of boundary integral equations leads to dense matrices, which would imply high computational complexity. Acceleration techniques, such as hierarchical matrix strategies combined with Adaptive Cross Approximation (ACA), are available in literature. Here we apply such a technique to the solution of an elastostatic problem, arising from industrial applications, posed at the surface of highly irregular cracks networks.
Highlights
Many applications involve the solution to an elliptic boundary value problem in a background medium perturbed by the presence of cracks that take the form of one or many pieces of surface
When the background medium can be considered as homogeneous, which is a valid approximation in many cases, boundary integral equations appear as a method of choice for the numerical solution to crack problems
This is the strategy adopted by IFP Energies Nouvelles (IFPEN) for the evolution of the deformation and perturbed stress field associated with the solution of an elastostatic problem around a network composed of multiple cracks
Summary
Many applications involve the solution to an elliptic boundary value problem in a background medium perturbed by the presence of cracks that take the form of one or many pieces of surface (with boundary). When the background medium can be considered as homogeneous, which is a valid approximation in many cases, boundary integral equations appear as a method of choice for the numerical solution to crack problems With such an approach, the problem is reformulated as a fully non-local equation posed at the surface of cracks. IFPEN did not adopt one of the currently available acceleration techniques mentioned above, but rather developed its own approach, which shall be referred to as “sparsification”, consisting in forcing coefficients of the BEM matrix to zero whenever the corresponding interaction involves sufficiently distant points of the computational domain This sparsification procedure is implementation friendly, and approximates the originally fully populated matrix with a sparse counterpart that allows fast matrix-vector products. We will present the sparsification heuristic used so far at IFPEN in order to decrease the algorithmic complexity of matrix-vector products
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