This paper reviews the state of the art and discusses recent developments in the field of
adaptive isogeometric analysis, with special focus on the mathematical theory. This includes …

Résumé We consider an adaptive isogeometric method (AIGM) based on (truncated)
hierarchical B-splines and present the study of its numerical properties. By following [10, 12 …

This paper presents an approach to generalize the concept of isogeometric analysis by
allowing different spaces for the parameterization of the computational domain and for the …

In this article we introduce all the ingredients to develop adaptive isogeometric methods
based on hierarchical B-splines. In particular, we give precise definitions of local refinement …

An adaptive higher-order method based on a generalization of polynomial/rational splines
over hierarchical T-meshes (PHT/RHT-splines) is introduced. While most problems …

The global (patch-wise) geometry map, which describes the computational domain, is a new
feature in isogeometric analysis. This map has a global tensor structure, inherited from the …

In the present work we introduce a complete set of algorithms to efficiently perform adaptive
refinement and coarsening by exploiting truncated hierarchical B-splines (THB-splines) …

One of the main topics of research on Isogeometric Analysis is local refinement. Among the
various techniques currently studied and developed, one of the most appealing, referred to …

Nonlinear behaviors are commonplace in many engineering applications, eg, metal forming
and vehicle crash tests. Different from linear systems, nonlinear problems cannot be solved …