An overview of the extended/generalized finite element method (GEFM/XFEM) with
emphasis on methodological issues is presented. This method enables the accurate …

An overview of computational methods to model fracture in brittle and quasi‐brittle materials
is given. The overview focuses on continuum models for fracture. First, numerical difficulties …

In this paper, we develop a dual‐horizon peridynamics (DH‐PD) formulation that naturally
includes varying horizon sizes and completely solves the 'ghost force'issue. Therefore, the …

The extended finite element method (X‐FEM) has proven to be an accurate, robust method
for solving problems in fracture mechanics. X‐FEM has typically been used with elements …

We introduce a new method for the numerical integration over curved surfaces and volumes
defined by a level set function. The method is based on the solution of a small linear system …

The advent of isogeometric analysis (IGA) using the same basis functions for design and
analysis constitutes a milestone in the unification of geometric modeling and numerical …

We introduce a new class of unfitted finite element methods with high order accurate
numerical integration over curved surfaces and volumes which are only implicitly defined by …

A high-order accurate numerical quadrature algorithm is presented for the evaluation of
integrals over curved surfaces and volumes which are defined implicitly via a fixed …

A unified strategy for the higher‐order accurate integration of implicitly defined geometries is
proposed. The geometry is represented by a higher‐order level‐set function. The task is to …

We construct efficient quadratures for the integration of polynomials over irregular convex
polygons and polyhedrons based on moment fitting equations. The quadrature construction …