Constructing efficient substructure-based preconditioners for BEM systems of equations.

*(English)*Zbl 1259.74040Summary: In this work, a generic substructuring algorithm is employed to construct global block-diagonal preconditioners for BEM systems of equations. In this strategy, the allowable fill-in positions are those on-diagonal block matrices corresponding to each BE subregion. As these subsystems are independently assembled, the preconditioner for a particular BE model, after the LU decomposition of all subsystem matrices, is easily formed. So as to highlight the efficiency of the preconditioning proposed, the Bi-CG solver, which presents a quite erratic convergence behavior, is considered. In the particular applications of this paper, 3D representative volume elements (RVEs) of carbon-nanotube (CNT) composites are analyzed. The models contain up to several tens of thousands of degrees of freedom. The efficiency and relevance of the preconditioning technique is also discussed in the context of developing general (parallel) BE codes.

##### MSC:

74S15 | Boundary element methods applied to problems in solid mechanics |

74E30 | Composite and mixture properties |

65F10 | Iterative numerical methods for linear systems |

##### Keywords:

3D boundary-element models; subregion-by-subregion algorithm; Krylov solvers; substructure-based block-diagonal preconditioners
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\textit{F. C. De Araújo} et al., Eng. Anal. Bound. Elem. 35, No. 3, 517--526 (2011; Zbl 1259.74040)

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