An adaptive interface-enriched generalized FEM for the treatment of problems with curved interfaces

Abstract

An adaptive refinement scheme is presented to reduce the geometry discretization error and provide higher-order enrichment functions for the interface-enriched generalized FEM. The proposed method relies on the h-adaptive and p-adaptive refinement techniques to reduce the discrepancy between the exact and discretized geometries of curved material interfaces. A thorough discussion is provided on identifying the appropriate level of the refinement for curved interfaces based on the size of the elements of the background mesh. Varied techniques are then studied for selecting the quasi-optimal location of interface nodes to obtain a more accurate approximation of the interface geometry. We also discuss different approaches for creating the integration sub-elements and evaluating the corresponding enrichment functions together with their impact on the performance and computational cost of higher-order enrichments. Several examples are presented to demonstrate the application of the adaptive interface-enriched generalized FEM for modeling thermo-mechanical problems with intricate geometries. The accuracy and convergence rate of the method are also studied in these example problems.