ECCOMAS 2024

Comparison of Integration Methods for Trimmed Elements

  • Teixeira, Guilherme Henrique (TU Graz)
  • Marussig, Benjamim (TU Graz)

Please login to view abstract download link

Defining a shape is the initial step for constructing an analysis model. In Computer Aided Design (CAD), the construction of a geometry is usually done through tensorproduct patches, which maps the shape from a parameter domain to the physical domain. However, using only a rectangular patch could be not enough to represent complex shapes. One way to deal with this situation and create complex geometries is to use trimming [1], a technique that involves defining a curve in the parameter domain and creating an interface that specifies which part of the parameter domain is visible or not. Since trimming is only a visualization solution, one of the problems faced in the analyses is the correction definition of the position of the quadrature points for integrating the trimmed elements. Faced with this situation, it is interesting to compare different tools that integrate these trimmed elements and choose the most suitable for the situation. This work aims to compare the integration of trimmed elements defined by implicit functions and B-splines. Our study focus on open-source tools such as Algoim [2] and Ginkgo (a new library for isogeometric analysis on Boolean operations with the interface to GeoPDEs [3, 4]). We compare the efficiency and robusten of these tools with numerical benchmarks REFERENCES [1] B. Marussig and J.R. Hughes, A Review of Trimming in Isogeometric Analysis: Challenges, Data Exchange and Simulation Aspects. Archives of Computational Methods in Engineering, Vol 25, pp. 1059–1127, 2018. [2] R. I. Saye, High-Order Quadrature Methods for Implicitly Defined Surfaces and Volumes in Hyperrectangles. SIAM Journal on Scientific Computing, Vol 37, pp. A993–A1019, 2015. [3] L. Coradello. Accurate isogeometric methods for trimmed shell structures. PhD Thesis, Lausanne EPFL ,2021. [4] R. Vazquez. A new design for the implementation of isogeometric analysis in Octaveand Matlab: GeoPDEs 3.0, Computers and Mathematics with Applications, Vol 72, pp. 523-554, 2016.