Elliptic homogenization problems in a domain Ω R d with n + 1 separate scales are reduced to elliptic problems in dimension (n + 1)d. These one-scale problems are discretized by a sparse tensor product finite element method (FEM). We prove that this sparse FEM has accuracy, work, and memory requirements comparable to those in a standard FEM for singlescale problems in Ω, while it gives numerica...

A node-based data structure is developed for use in either two-dimensional (2-D) or three-dimensional (3-D) ®nite element method (FEM) problems. This grid uses quadrilateral (2-D) or hexahedral (3-D) elements and is dynamically adaptive according to the 1-irregular requirement for re®nement±dere®nement. Implemented in C 1 1 , the grid consists of node objects linked with pointers to neighboring...

An algorithm for non-intrusively coupling a commercial finite element software with a research code implementing a hierarchical enrichment of finite element spaces is presented. Examples of hierarchical methods supported by the algorithm are the Generalized or eXtended FEM (GFEM), the scale-bridging GFEM with numerically defined enrichment functions (GFEMgl), and the p-version of the FEM. The p...

This study presents an adaptive coupling peridynamic least-square minimization with the finite element method (PDLSM-FEM) for fracture analysis. The presented utilizes PDLSM modeling discontinuities while maximizing FEM region computational efficiency. Within PDLSM-FEM, only elements intersecting crack path and their neighboring are defined as PD elements, whose stiffness matrices derived based...

Dynamic NURBS, also called D-NURBS, is a known dynamic version of the nonuniform rational B-spline (NURBS) which integrates free-form shape representation and a physically-based model in a unified framework. More recently, computer aided design (CAD) and finite element (FEM) community realized the need to unify CAD and FEM descriptions which motivates a review of D-NURBS concepts. Therefore, in...

A new nite element method for elliptic problems with locally periodic microstructure of length " > 0 is developed and analyzed. It is shown that the method converges, as " ! 0, to the solution of the homogenized problem with optimal order in " and exponentially in the number of degrees of freedom independent of " > 0. The computational work of the method is bounded independently of ". Numerical...

Three case studies involving the use of numerical models are presented in this paper. First, a comparison of FE modelling of a deep excavation is made using 2-D finite element software, SAGE-CRISP and PLAXIS. In the second study, benchmarking is made between results obtained from 2-D FE modelling using PLAXIS and well-established 3-D centrifuge studies for the case of an existing single pile an...