Revisiting the BE SBS algorithm and applying it to solve torsion problems in composite bars: robustness and efficiency study. (English) Zbl 1464.74259

Summary: The construction of truly competitive boundary-element (BE) codes, capable of analyzing real-life engineering problems, unavoidably requires the devising of coupling strategies to make the modeling of complex heterogeneous domains user-friendly. Thereby, high-performance algorithms for solving the highly sparse resulting system of equations are essential. Moreover, as discontinuous boundary elements are necessary to alleviate the modeling process of coupled domains, efficient (low-order) quadratures for integrating singular and nearly-singular fundamental kernels over the boundary elements must be implemented. This paper newly discusses the construction of the boundary-element subregion-by-subregion (BE SBS) technique based on a BEM formulation for torsion problems in general composite bars. One also presents details of the formulation of the Krylov solvers BiCG and BiCGSTAB-\((l)\), embedded in the coupling algorithm. In addition, the BE SBS matrix structure itself is used to form an efficient sparse incomplete LU factorization (SILU) preconditioner to accelerate the iterative solution process. Torsion problems in bars with complex composite patterns (e.g. with many different materials) are analyzed to attest the efficiency and robustness of the whole boundary-element technique.


74S15 Boundary element methods applied to problems in solid mechanics
65N38 Boundary element methods for boundary value problems involving PDEs
74K10 Rods (beams, columns, shafts, arches, rings, etc.)


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