Algebraic Dual Polynomials for the Equivalence of Curl-Curl Problems

Marc Gerritsma; Varun Jain; Yi Zhang; Artur Palha

doi:10.1007/978-3-030-30705-9_27

Algebraic Dual Polynomials for the Equivalence of Curl-Curl Problems

Marc Gerritsma^*, Varun Jain, Yi Zhang, Artur Palha

^*Corresponding author for this work

Aerodynamics

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

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.

Original language	English
Title of host publication	Numerical Methods for Flows - FEF 2017 Selected Contributions
Editors	Harald van Brummelen, Alessandro Corsini, Simona Perotto, Gianluigi Rozza
Publisher	Springer Open
Pages	307-320
Number of pages	14
ISBN (Print)	9783030307042
DOIs	https://doi.org/10.1007/978-3-030-30705-9_27
Publication status	Published - 2020
Event	19th International Conference on Finite Elements in Flow Problems, FEF 2017 - Rome, Italy Duration: 5 Apr 2017 → 7 Apr 2017

Publication series

Name	Lecture Notes in Computational Science and Engineering
Volume	132
ISSN (Print)	1439-7358
ISSN (Electronic)	2197-7100

Conference

Conference	19th International Conference on Finite Elements in Flow Problems, FEF 2017
Country/Territory	Italy
City	Rome
Period	5/04/17 → 7/04/17

Keywords

Algebraic dual polynomials
Curl-curl problems
Spectral element method

Access to Document

10.1007/978-3-030-30705-9_27

Cite this

Gerritsma, M., Jain, V., Zhang, Y., & Palha, A. (2020). Algebraic Dual Polynomials for the Equivalence of Curl-Curl Problems. In H. van Brummelen, A. Corsini, S. Perotto, & G. Rozza (Eds.), Numerical Methods for Flows - FEF 2017 Selected Contributions (pp. 307-320). (Lecture Notes in Computational Science and Engineering; Vol. 132). Springer Open. https://doi.org/10.1007/978-3-030-30705-9_27

Gerritsma, Marc ; Jain, Varun ; Zhang, Yi ; Palha, Artur. / Algebraic Dual Polynomials for the Equivalence of Curl-Curl Problems. Numerical Methods for Flows - FEF 2017 Selected Contributions. editor / Harald van Brummelen ; Alessandro Corsini ; Simona Perotto ; Gianluigi Rozza. Springer Open, 2020. pp. 307-320 (Lecture Notes in Computational Science and Engineering).

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title = "Algebraic Dual Polynomials for the Equivalence of Curl-Curl Problems",

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= {\^E}⊣ on E and Neumann boundary conditions n×curlF={\^E}⊣, 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.",

keywords = "Algebraic dual polynomials, Curl-curl problems, Spectral element method",

author = "Marc Gerritsma and Varun Jain and Yi Zhang and Artur Palha",

year = "2020",

doi = "10.1007/978-3-030-30705-9_27",

language = "English",

isbn = "9783030307042",

series = "Lecture Notes in Computational Science and Engineering",

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booktitle = "Numerical Methods for Flows - FEF 2017 Selected Contributions",

address = "United Kingdom",

note = "19th International Conference on Finite Elements in Flow Problems, FEF 2017 ; Conference date: 05-04-2017 Through 07-04-2017",

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Gerritsma, M , Jain, V , Zhang, Y & Palha, A 2020, Algebraic Dual Polynomials for the Equivalence of Curl-Curl Problems. in H van Brummelen, A Corsini, S Perotto & G Rozza (eds), Numerical Methods for Flows - FEF 2017 Selected Contributions. Lecture Notes in Computational Science and Engineering, vol. 132, Springer Open, pp. 307-320, 19th International Conference on Finite Elements in Flow Problems, FEF 2017, Rome, Italy, 5/04/17. https://doi.org/10.1007/978-3-030-30705-9_27

Algebraic Dual Polynomials for the Equivalence of Curl-Curl Problems. / Gerritsma, Marc ; Jain, Varun ; Zhang, Yi ; Palha, Artur.

Numerical Methods for Flows - FEF 2017 Selected Contributions. ed. / Harald van Brummelen; Alessandro Corsini; Simona Perotto; Gianluigi Rozza. Springer Open, 2020. p. 307-320 (Lecture Notes in Computational Science and Engineering; Vol. 132).

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

TY - GEN

T1 - Algebraic Dual Polynomials for the Equivalence of Curl-Curl Problems

AU - Gerritsma, Marc

AU - Jain, Varun

AU - Zhang, Yi

AU - Palha, Artur

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

KW - Algebraic dual polynomials

KW - Curl-curl problems

KW - Spectral element method

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U2 - 10.1007/978-3-030-30705-9_27

DO - 10.1007/978-3-030-30705-9_27

M3 - Conference contribution

AN - SCOPUS:85081714444

SN - 9783030307042

T3 - Lecture Notes in Computational Science and Engineering

SP - 307

EP - 320

BT - Numerical Methods for Flows - FEF 2017 Selected Contributions

A2 - van Brummelen, Harald

A2 - Corsini, Alessandro

A2 - Perotto, Simona

A2 - Rozza, Gianluigi

PB - Springer Open

T2 - 19th International Conference on Finite Elements in Flow Problems, FEF 2017

Y2 - 5 April 2017 through 7 April 2017

ER -

Algebraic Dual Polynomials for the Equivalence of Curl-Curl Problems

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