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    Item type:Publication, Access status: without files ,
    Equivalent Legendre polynomials: Numerical integration of discontinuous functions in the finite element methods
    (2019-01)
    Abedian, Alireza
    ;
    Düster, Alexander
    The efficiency of numerical integration of discontinuous functions is a challenge for many different computational methods. To overcome this problem, we introduce an efficient and simple numerical method for the integration of discontinuous functions on an arbitrary domain. In the proposed method, the discontinuous function over the domain is replaced by a continuous equivalent function using Legendre polynomials. The method is applicable to all Ansatz spaces with continuous basis functions, and it allows to use standard numerical integration methods in the entire domain. This imposed continuous function is called equivalent Legendre polynomial (ELP). Several numerical examples serve to demonstrate the efficiency and accuracy of the proposed method. Based on 2D and 3D problems of linear elastostatics, the introduced method is further evaluated in the concept of the fictitious domain finite element methods.
    Publicationtype: Journal Article
      234
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    Item type:Publication, Access status: without files ,
    Numerical integration of discontinuous functions: moment fitting and smart octree
    (Springer, 2017-07-18)
    Hubrich, Simeon
    ;
    Di Stolfo, Paolo
    ;
    Kudela, Laszlo
    ;
    Kollmannsberger, Stefan
    ;
    Rank, Ernst
    A fast and simple grid generation can be achieved by non-standard discretization methods where the mesh does not conform to the boundary or the internal interfaces of the problem. However, this simplification leads to discontinuous integrands for intersected elements and, therefore, standard quadrature rules do not perform well anymore. Consequently, special methods are required for the numerical integration. To this end, we present two approaches to obtain quadrature rules for arbitrary domains. The first approach is based on an extension of the moment fitting method combined with an optimization strategy for the position and weights of the quadrature points. In the second approach, we apply the smart octree, which generates curved sub-cells for the integration mesh. To demonstrate the performance of the proposed methods, we consider several numerical examples, showing that the methods lead to efficient quadrature rules, resulting in less integration points and in high accuracy.
    Publicationtype: Journal Article
      246