  The Finite Cell Method (FCM) together with Isogeometric analysis (IGA) has
been applied successfully in various problems in solid mechanics, in
image-based analysis, fluid-structure interaction and in many other
applications. A challenging aspect of the isogeometric finite cell method is
the integration of cut cells. In particular in three-dimensional simulations
the computational effort associated with integration can be the critical
component of a simulation. A myriad of integration strategies has been proposed
over the past years to ameliorate the difficulties associated with integration,
but a general optimal integration framework that suits a broad class of
engineering problems is not yet available. In this contribution we provide a
thorough investigation of the accuracy and computational effort of the octree
integration scheme. We quantify the contribution of the integration error using
the theoretical basis provided by Strang's first lemma. Based on this study we
propose an error-estimate-based adaptive integration procedure for immersed
isogeometric analysis. Additionally, we present a detailed numerical
investigation of the proposed optimal integration algorithm and its application
to immersed isogeometric analysis using two- and three-dimensional linear
elasticity problems.
