The Use of Dual B-Spline Representations for the Double de Rham Complex of Discrete Differential Forms

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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.

Original languageEnglish
Title of host publicationIsogeometric Analysis and Applications 2018
EditorsHarald van Brummelen, Cornelis Vuik, Matthias Möller, Clemens Verhoosel, Bernd Simeon, Bert Jüttler
PublisherSpringer
Pages227-242
Number of pages16
ISBN (Print)9783030498351
DOIs
Publication statusPublished - 2021
Event3rd Conference on Isogeometric Analysis and Applications, 2018 - Delft, Netherlands
Duration: 23 Apr 201826 Apr 2018

Publication series

NameLecture Notes in Computational Science and Engineering
Volume133
ISSN (Print)1439-7358
ISSN (Electronic)2197-7100

Conference

Conference3rd Conference on Isogeometric Analysis and Applications, 2018
CountryNetherlands
CityDelft
Period23/04/1826/04/18

Keywords

  • B-splines
  • Differential forms
  • Discrete double de Rham complex
  • Dual representations

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