Algebraic Dual Polynomials for the Equivalence of Curl-Curl Problems

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Algebraic Dual Polynomials for the Equivalence of Curl-Curl Problems

Conference Paper (2020)

Author(s)

Marc Gerritsma (TU Delft - Aerospace Engineering)

Varun Jain (TU Delft - Aerospace Engineering)

Yi Zhang (TU Delft - Aerospace Engineering)

Artur Palha (Eindhoven University of Technology)

Research Group

Aerodynamics

Spectral element method Algebraic dual polynomials Curl-curl problems

DOI related publication

https://doi.org/10.1007/978-3-030-30705-9_27 Final published version

To reference this document use

https://resolver.tudelft.nl/uuid:517b465a-7ed9-45f5-85e9-92a18712ec77

More Info

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Publication Year

2020

Language

English

Abstract

In this paper we will consider two curl-curl equations in two dimensions. One curl-curl problem for a scalar quantity F and one problem for a vector field E. For Dirichlet boundary conditions n× E= Ê_⊣ on E and Neumann boundary conditions n×curlF=Ê⊣, we expect the solutions to satisfy E = curl F. When we use algebraic dual polynomial representations, these identities continue to hold at the discrete level. Equivalence will be proved and illustrated with a computational example.