Selective Enrichment of Moment Fitting for the Quadrature of Cut Finite Elements and Cells

KeyWords: Moment Fitting, Enrichment, Finite Cell Method, High-Order, Numerical Integration, Material Interfaces For generalized or extended finite element methods and fictitious domain methods, the integration of discontinuous functions still poses a challenge. In the finite cell method [1, 2], for example, the integration of cells intersected by the boundary of the domain or by material interfaces can easily dominate the computational effort and accuracy of the overall discretization approach. To this end, we propose an improved moment fitting scheme which is applicable to high-order methods and allows to treat discontinuities on curved surfaces in an efficient and accurate manner [3]. The presented approach also circumvents the solution of a linear system to compute the desired weights of the quadrature rule. Furthermore, we enrich the basis functions of the moment fitting in order to be able to capture different kinds of discontinuities. The related overhead for the computation of the desired quadrature rule is rather small and can be amortized during the costly integration of high-order stiffness matrices. Further savings of computational effort are to be expected, when re-using the derived quadrature rule for nonlinear problems, where the stiffness matrix has to be re-computed many times. We will present several numerical examples ranging from 1D to 3D where different discontinuous functions defined on curved surfaces are integrated with the proposed enriched moment fitting method. Possible applications are, for example, problems with material interfaces, where a combination of the enrichment of the displacement field together with the selective integration of the discontinuous integrand of the stiffness matrix results in an efficient discretization approach. REFERENCES [1] Parvizian, J. and D¨uster, A. and Rank, E. Finite cell method – h- and p-extension for embedded domain problems in solid mechanics. Comput. Mech. (2007) 41:121–133. [2] D¨uster, A. and Parvizian, J. and Yang, Z. and Rank, E. The finite cell method for three-dimensional problems of solid mechanics. Comput. Methods Appl. Mech. Eng. (2008) 197:3768–3782. [3] D¨uster, A. and Allix, O. Selective enrichment of moment fitting and application to cut finite elements and cells. Comput. Mech. (2019) https://doi.org/10.1007/s00466-019-01776-2

O. Allix (1) , A Düster

1 LMT - Laboratoire de mécanique et technologie

Domaines: Sciences de l'ingénieur [physics]

O. Allix, A Düster. Selective Enrichment of Moment Fitting for the Quadrature of Cut Finite Elements and Cells. 14th World Congress on Computational Mechanics (WCCM) ECCOMAS Congress 2020, Jan 2021, Paris, France. ⟨hal-03118207⟩