Abstract
One question in the context of immersed boundary or fictitious domain methods is how to compute discontinuous integrands in cut elements accurately. A frequently used method is to apply a composed Gaussian quadrature based on a spacetree subdivision. Although this approach works robustly on any geometry, the resulting integration mesh yields a low order representation of the boundary. If high order shape functions are employed to approximate the solution, this lack of geometric approximation power prevents exponential convergence in the asymptotic range. In this paper we present an algorithmic subdivision approach that aims to be as robust as the spacetree decomposition even for close-to-degenerate cases—but remains geometrically accurate at the same time. Based on 2D numerical examples, we will show that optimal convergence rates can be obtained with a nearly optimal number of integration points.
Highlights
One of the essential steps of performing a finite element analysis is the discretisation of the geometric domain into an analysis-suitable mesh
In order to improve the precision of the numerical integration, the Finite Cell Method (FCM) uses a composed Gaussian quadrature that is based on a spacetree decomposition of the cells that are cut by the domain boundaries
The standard integration in FCM is performed by a spacetree based composed Gaussian quadrature, which works robustly on any geometry, but lacks the geometric approximation power that balances well with the high order shape functions of p-FEM
Summary
One of the essential steps of performing a finite element analysis is the discretisation of the geometric domain into an analysis-suitable mesh. In order to improve the precision of the numerical integration, the FCM uses a composed Gaussian quadrature that is based on a spacetree decomposition of the cells that are cut by the domain boundaries. For the same error in the strain energy, the blended integration cells require approximately one order of magnitude less Gauss points than a quadtree integration mesh with a depth of k = 4. It is worth noting here that an integration mesh with blended elements including breakpoint subdivision and 7 × 7 quadrature points per integration cell yields approximately 3.5 times less integration points in comparison to the quadtree based integration with a refinement level of k = 4.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Advanced Modeling and Simulation in Engineering Sciences
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
