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

Conference paper (2021)

Authors

Y. Zhang Aerodynamics - Aerospace Engineering
V. Jain Aerodynamics - Aerospace Engineering
A. Palha Aerodynamics - Aerospace Engineering
M.I. Gerritsma Aerodynamics - Aerospace Engineering
Research Group
Aerodynamics (Aerospace Engineering) (TU Delft)
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Published Date

2021

Language

English

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Faculty

Aerospace Engineering

Department

Flow Physics and Technology

Research Group

Aerodynamics

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.

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