The Use of Dual B-Spline Representations for the Double de Rham Complex of Discrete Differential Forms
More Info
expand_more
expand_more
Abstract
In ℝn, let Λk(Ω) represent the space of smooth differential k-forms in Ω. The de Rham complex consists of a sequence of spaces, Λk(Ω), k = 0, 1…, n, connected by the exterior derivative, d: Λk(Ω) → Λk+1(Ω). 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.
Files
Zhang2021_Chapter_TheUseOfDual... (.pdf)
(.pdf | 1.09 Mb)
Download not available