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Fast isogeometric boundary element method based on independent field approximation. (English) Zbl 1423.74101
Summary: An isogeometric boundary element method for problems in elasticity is presented, which is based on an independent approximation for the geometry, traction and displacement field. This enables a flexible choice of refinement strategies, permits an efficient evaluation of geometry related information, a mixed collocation scheme which deals with discontinuous tractions along non-smooth boundaries and a significant reduction of the right hand side of the system of equations for common boundary conditions. All these benefits are achieved without any loss of accuracy compared to conventional isogeometric formulations. The system matrices are approximated by means of hierarchical matrices to reduce the computational complexity for large scale analysis. For the required geometrical bisection of the domain, a strategy for the evaluation of bounding boxes containing the supports of NURBS basis functions is presented. The versatility and accuracy of the proposed methodology are demonstrated by convergence studies showing optimal rates and real world examples in two and three dimensions.

MSC:
74B05 Classical linear elasticity
65D17 Computer-aided design (modeling of curves and surfaces)
65N38 Boundary element methods for boundary value problems involving PDEs
74S15 Boundary element methods applied to problems in solid mechanics
Software:
hlib
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