cite as


    author="Zhang, Yi
    and Jain, Varun
    and Palha, Artur
    and Gerritsma, Marc",
    editor="van Brummelen, Harald
    and Vuik, Cornelis
    and M{\"o}ller, Matthias
    and Verhoosel, Clemens
    and Simeon, Bernd
    and J{\"u}ttler, Bert",
    title="The Use of Dual B-Spline Representations for the Double de Rham Complex of Discrete Differential Forms",
    booktitle="Isogeometric Analysis and Applications 2018",
    publisher="Springer International Publishing",
    abstract="In ℝn{\$}{\$} {\backslash}mathbb {\{}R{\}}^n {\$}{\$}, let $\Lambda$k({\thinspace}$\Omega$) represent the space of smooth differential k-forms in $\Omega$. The de Rham complex consists of a sequence of spaces, $\Lambda$k({\thinspace}$\Omega$), k{\thinspace}={\thinspace}0, 1{\ldots}, n, connected by the exterior derivative, d: $\Lambda$k({\thinspace}$\Omega$){\thinspace}{\textrightarrow} $\Lambda$k+1({\thinspace}$\Omega$). Appropriately chosen B-spline spaces together with their associated dual B-spline spaces form a discrete double de Rham complex. In practical applications, this discrete double de Rham complex leads to very sparse systems. In this paper, this construction will be explained and illustrated by means of a non-trivial three-dimensional example.",