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A SBS-BD based solver for domain decomposition in BE methods. (English) Zbl 1287.65131
Summary: In boundary element methods (BEM), subregioning may be needed either to model complex solids (with cracks, stiffeners, layers, inclusions, etc.) or simply to decompose a problem by computational reasons (e.g. for parallelization). Since the development of the first BEM codes, many attempts have been made to efficiently devise generic boundary-element subregioning techniques. Crucial points are how to profit from the sparsity of the global matrix, and how to deal with traction discontinuities. In this work, the most fundamental steps for efficiently devising reliable and efficient subregioning algorithms are discussed. The subregion-by-subregion (SBS) algorithm and the preconditioning of the embedded Krylov solver are addressed. Besides the BiCG solver, the BiCGSTAB(\(l\)) is newly incorporated into the BE-SBS code. The 3D microstructural analysis of carbon-nanotube-reinforced composites (CNT composites) is considered to verify the performance of the algorithm. Numerical results showing the efficiency of the preconditioned solvers studied are presented.

MSC:
65N38 Boundary element methods for boundary value problems involving PDEs
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
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