Fractures have attracted the attention of computational scientists for several decades. The
modeling and simulation of fractures have been a major motivation for developing enriched …

Abstract A three-dimensional (3D) slope stability analysis method is presented in this paper
based on three-dimensional independent cover based manifold method (ICMM3D) and …

Although its unprecedentedly success in approximating the singular field around a crack tip
independent of mesh discretization, XFEM still has been long hindered in engineering …

We propose a novel Gaussian quadrature, referred to as the learned Gaussian quadrature,
that is obtained by employing a supervised learning algorithm to find improved weights for …

We present a combination of techniques to improve the convergence and conditioning
properties of partition of unity (PU) enriched finite element methods. By applying these …

Modeling and prediction of dynamic behaviors of cracked bodies are vital to the safety
evaluation of structures. The numerical manifold method (NMM) has achieved considerable …

Modelling heat conduction is of significant importance for evaluating temperature effects of
granular materials. Since the randomness of the grain structure and the heat resistance …

A GFEM without extra dof is developed. Without the extra dof, the resulting linear system
becomes independent—in size—of the order of local approximation, the resulting PU …

Numerous approaches have been proposed to enhance the accuracy and convergence of
the numerical manifold method (NMM) in recent years, but most, if not all, of these …

The numerical manifold method (NMM) is explored for simulations of bimaterial interface
cracks. Two special types of physical covers with customized cover functions are introduced …