Multi-inclusions modeling by adaptive XIGA based on LR B-splines and multiple level sets

In this paper, we present an effective computational approach that combines an adaptive extended isogeometric analysis (XIGA) method with locally refined (LR) B-splines and level set methods for modeling multiple inclusions in two-dimensional (2D) elasticity problems. The advantage of XIGA is to model inclusions without considering internal inclusion interfaces by additional functions. Multiple level set functions are used to represent the location of inclusion interfaces and to define enrichment functions. Local refinement for adaptive XIGA using LR B-splines is based on the posterior error estimator. We use the strategy of structured mesh refinement to implement local refinement in adaptive XIGA. Numerical experiments for multiple inclusions with complicated geometries are presented to demonstrate the accuracy and performance of the proposed approach. In addition, numerical results indicate that the adaptive XIGA with local refinement achieves faster convergence rate than that of the XIGA with uniform global refinement.