Adaptive quadrature of trimmed finite elements and cells based on bezier approximation

In this paper, a new boundary-conforming adaptive method for the numerical integration of trimmed elements is presented. The locations and weights of new integration points are determined based on special mapping formulations. The prerequisite of this technique is to describe the trimming curves/surfaces by parametric Bezier curves/surfaces within the parent element domain. The fitting error is under control, therefore the number of quadrature points for exact integration can be adjusted automatically based on the complexity of trimming curve and the corresponding integrand. The proposed method can be easily implemented into fictitious domain approaches. Different integration tasks as well as structural examples reveal that the proposed method delivers accurate and robust solutions for a wide variety of 2D/3D geometries with a rather low number of integration points.

Subjects

Adaptive Gaussian integration

Bezier functions

finite cell method

DDC Class

624: Civil Engineering, Environmental Engineering

690: Building, Construction

Options

Adaptive quadrature of trimmed finite elements and cells based on bezier approximation