GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Computer Methods in Applied Mechanics and Engineering
A fast algorithm for particle simulations
Journal of Computational Physics
Parallel Preconditioning with Sparse Approximate Inverses
SIAM Journal on Scientific Computing
Iterative methods for solving linear systems
Iterative methods for solving linear systems
A Sparse Approximate Inverse Preconditioner for Nonsymmetric Linear Systems
SIAM Journal on Scientific Computing
Programming the Boundary Element Method
Programming the Boundary Element Method
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
A fast elasto-plastic formulation with hierarchical matrices and the boundary element method
Computational Mechanics
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BEM-FEM coupling is desirable for three-dimensional problems involving specific features such as (i) large or unbounded media with linear constitutive properties, (ii) cracks, (iii) critical parts of complex geometry requiring accurate stress analyses. However, for cases with a BEM discretization involving a large number N"B"E"M of degrees of freedom, setting up the BEM contribution to the coupled problem using conventional techniques is an expensive O(N"B"E"M^2) task. Moreover, the fully-populated BEM block entails a O(N"B"E"M^2) storage requirement and a O(N"B"E"M^3) contribution to the solution time via usual direct solvers. To overcome these pitfalls, the BEM contribution is formulated using the fast multipole method (FMM) and the coupled equations are solved by means of an iterative GMRES solver. Both the storage requirements and the solution times are found to be close to O(N"B"E"M). A preconditioner based on the sparse approximate inverse of the BEM block is shown to improve the convergence of the GMRES solver. Numerical examples involving N"B"E"M=O(10^5-10^6) unknowns, run on a PC computer, are presented; they include the Eshelby inclusion (as a validation example), a many-inclusion configuration, and a dam structure.