A High-Order Generalized/eXtended FEM for Three-Dimensional Problems with Material Interfaces
Please login to view abstract download link
The high-order p-hierarchical Generalized/eXtended Finite Element Method (G/XFEM) proposed in [1] is explored to solve three-dimensional (3-D) problems containing a distribution of material interfaces, voids, and inclusions. The adopted G/XFEM augments p-hierarchical FEM bases, spanned by hierarchical vertex, edge, face, and volume shape functions, and generates hierarchical enriched shape functions that can accurately approximate the weak discontinuities introduced by material interfaces. Moreover, the type of enrichment function proposed in [1] and adopted in this work ensures that both first- and second-order formulations are well-conditioned. Finally, coupling the proposed G/XFEM with a computationally efficient preconditioner based on local eigendecompositions of the stiffness matrix allows higher-order formulations, with p > 2, to be also well-conditioned. To improve computational efficiency in 3-D problems, an explicit-implicit way of representing 3-D interfaces is also proposed herein. Furthermore, computational aspects regarding numerical integration and the implementation of the adopted local preconditioner in a sparse data structure are provided. 3-D numerical experiments are adopted to show convergence and conditioning aspects of the proposed G/XFEMs.
