Given a topological complex M with glueing data along edges shared by adjacent faces, we
study the associated space of geometrically smooth spline functions that satisfy …

We propose a numerical treatment for the geometric singularity at the polar grid center
encountered in the application of the isoparametric bi-cubic Hermite Bézier finite element …

We present an m-adic Newton iteration with quadratic convergence for lexicographic
Gröbner basis of zero dimensional ideals in two variables. We rely on a structural result …

Motivated by the magneto hydrodynamic (MHD) simulation for Tokamaks with Isogeometric
analysis, we present splines defined over a rectangular mesh with a complex topological …

A computationally challenging classical elimination theory problem is to compute
polynomials which vanish on the set of tensors of a given rank. By moving away from …

A new aerofoil parameterisation method is put forward to represent an aerofoil by combining
the leading edge modification class/shape function transformation (LEM CST) method and …

Many algorithms for determining properties of semi-algebraic sets rely upon the ability to
compute smooth points [1]. We present a simple procedure based on computing the critical …

The urging quest for diminishing the gap between finite element methods and computer-
aided design is growing every day. Isogeometric analysis is driving that search a step …

In this paper we provide a new method to certify that a nearby polynomial system has a
singular isolated root and we compute its multiplicity structure. More precisely, given a …

Given a well-constrained polynomial system $ f $ associated with a simple multiple zero $ x
$ of multiplicity $\mu $, we give a computable separation bound for isolating $ x $ from the …