Numerical integration for nonlinear problems of the finite cell method using an adaptive scheme based on moment fitting

Abstract

Fictitious domain methods such as the finite cell method simplify the discretization process significantly as the mesh is decoupled from the geometrical description. However, this simplification in the mesh generation results in broken cells, which is why special integration methods are required. Usually, adaptive integration schemes are applied resulting in a large number of integration points and, thus, an expensive numerical integration — especially for nonlinear applications. To perform the numerical integration more efficiently, we propose an adaptive integration method using moment fitting. Thereby, we present a moment fitting approach based on Lagrange polynomials through Gauss–Legendre points to circumvent having to solve the moment fitting equation system. The performance of this integration method is shown by studying several numerical examples of the finite cell method for small and large strain problems in elastoplasticity.