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Smart octrees: accurately integrating discontinuous functions in 3D. (English) Zbl 1436.65022
Summary: This paper presents an efficient and accurate method for the integration of discontinuous functions on a background mesh in three dimensions. This task is important in computational mechanics applications where internal interfaces are present in the computational domain. The proposed method creates boundary-conforming integration subcells for composed numerical quadrature, even in the presence of sharp geometric features (e.g. edges or vertices). Similar to the octree procedure, the algorithm subdivides the cut elements into eight octants. However, the octant nodes are moved onto the interface, which allows for a robust resolution of the intersection topology in the element while maintaining algorithmic simplicity. Numerical examples demonstrate that the method is able to deliver highly accurate domain integrals with a minimal number of quadrature points. Further examples show that the proposed method provides a viable alternative to standard octree-based approaches when combined with the Finite Cell Method.

65D30 Numerical integration
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
74S05 Finite element methods applied to problems in solid mechanics
65D17 Computer-aided design (modeling of curves and surfaces)
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