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

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

Conference Paper (2021)

Author(s)

Yi Zhang (TU Delft - Aerospace Engineering)

Varun Jain (TU Delft - Aerospace Engineering)

Artur Palha (TU Delft - Aerospace Engineering)

Marc Gerritsma (TU Delft - Aerospace Engineering)

Research Group

Aerodynamics

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

DOI related publication

https://doi.org/10.1007/978-3-030-49836-8_11 Final published version

To reference this document use

https://resolver.tudelft.nl/uuid:ca4243b0-2189-4813-991c-4d06d5336dd4

More Info

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Publication Year

2021

Language

English

Abstract

In ℝⁿ, let Λ^k(Ω) represent the space of smooth differential k-forms in Ω. The de Rham complex consists of a sequence of spaces, Λ^k(Ω), k = 0, 1…, n, connected by the exterior derivative, d: Λ^k(Ω) → Λ^k+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.