Adaptive Quadrature and Remeshing Strategies for the Finite Cell Method at Large Deformations

Abstract

Numerical methods based on a fictitious domain approach, such as the finite cell method, simplify the meshing process significantly as the mesh does not need to conform to the geometry of the underlying problem. However, such methods result in elements/cells which are intersected by the domain boundary. Consequently, special integration methods have to be applied for the broken elements/cells to achieve accurate results. One of the methods that is commonly used in the finite cell method is an adaptive scheme based on a spacetree decomposition. Unfortunately, it results in a large number of integration points which makes the method quite expensive. In the first part of this contribution, we try to overcome this problem by introducing an adaptive scheme for the moment fitting to be able to integrate broken cells efficiently and robustly for nonlinear problems. Furthermore, a remeshing strategy for the finite cell method will be introduced to improve the solution quality and overcome the large distortion of the mesh during the simulation which can cause the analysis to fail. To this end, a new mesh with a good quality is created whenever the old mesh is no longer capable of taking any further deformations. Afterwards, a data transfer between the old and the new meshes is performed with the help of a local radial basis function interpolation. Different numerical examples are presented to study the performance of the proposed methods.