On the similarities and differences between Classical Hierarchical, Truncated Hierarchical and LR B-splines

Abstract

a b s t r a c tSynthetic amorphous silica (SAS) like NM-200 is used in a wide variety of technological applications and consumer products. Although SAS has been widely investigated the available reproductive toxicity studies are old and do not cover all requirements of current OECD Guidelines. As part of a CEFIC-LRI project, NM-200 was tested in a two-generation reproduction toxicity study according to OECD guideline 416. Male and female rats were treated by oral gavage with NM-200 at dose levels of 0, 100, 300 and 1000 mg/kg bw/day for two generations. Body weight and food consumption were measured throughout the study. Reproductive and developmental parameters were measured and at sacrifice (reproductive) organs and tissues were sampled for histopathological analysis. Oral administration of NM-200 up to 1000 mg/kg bw/day had no adverse effects on the reproductive performance of rats or on the growth and development of the offspring into adulthood for two consecutive generations. The NOAEL was 1000 mg/kg body weight per day.

A variational method to avoid locking—independent of the discretization scheme

“…The idea of using splines in finite-element analysis (see, for instance, the work of Höllig 7 and the references therein) has experienced its breakthrough with the development of isogeometric analysis (IGA), proposed in the seminal work of Hughes et al 8 Since then, numerous contributions have dealt with structural mechanics problems solved by spline-based finite-element methods. Up to now, a large number of different spline spaces have been introduced in the context of IGA for solids and structures, for instance (trimmed) B-splines/NURBS, hierarchically refined B-splines, T-splines, Powell-Sabin splines and their non-uniform rational version NURPS, PHT-splines, and LRB-splines, among others (see, for example, other works [9][10][11][12][13][14][15][16][17][18][19][20][21] ).…”

Divergence-conforming discretization for Stokes problem on locally refined meshes using LR B-splines

“…We note that the structured LR B-splines and Hierarchical refined B-splines may produce similar meshes. However, as shown in [36] they are in general not identical, and they produce finite element matrices with different sparsity patterns and conditioning numbers. Proof.…”

Discrete fracture analysis using locally refined T‐splines

“…In this contribution, we will use locally refined (LR) T‐splines to initiate and propagate a discontinuity. LR T‐splines are a combination of T‐splines and LR B‐splines, where the latter are obtained by locally enriching the space of the basis functions by replacing coarse‐grid B‐splines by fine‐grid B‐splines . LR T‐splines are constructed by meshline insertions into an initial T‐mesh.…”