An Embedded Compact Scheme for Biharmonic Problems in Irregular Domains

Matania Ben-Artzi; Jean Pierre Croisille; Dalia Fishelov

doi:10.1007/978-3-319-65530-7_2

An Embedded Compact Scheme for Biharmonic Problems in Irregular Domains

Matania Ben-Artzi
, Jean Pierre Croisille^*
, Dalia Fishelov

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

2 Scopus citations

Abstract

In Ben-Artzi et al. (SIAM J Numer Anal 47:3087–3108 (2009), [1]) a Cartesian embedded finite difference scheme for biharmonic problems has been introduced. The design of the scheme relies on a 19-dimensional polynomial space. In this paper, we show how to simplify the implementation by introducing a directional decomposition of this space. The boundary is handled via a level-set approach. Numerical results for non convex domains demonstrate the fourth order accuracy of the scheme.

Original language	English
Title of host publication	Advanced Computing in Industrial Mathematics - 11th Annual Meeting of the Bulgarian Section of SIAM, Revised Selected Papers
Editors	Michail Todorov, Ivan Georgiev, Krassimir Georgiev, Ivan Georgiev
Publisher	Springer Verlag
Pages	11-23
Number of pages	13
ISBN (Print)	9783319655291
DOIs	https://doi.org/10.1007/978-3-319-65530-7_2
State	Published - 2018
Event	11th Annual Meeting of the Bulgarian Section of the Society for Industrial and Applied Mathematics, BGSIAM 2016 - Sofia, Bulgaria Duration: 20 Dec 2016 → 22 Dec 2016

Publication series

Name	Studies in Computational Intelligence
Volume	728
ISSN (Print)	1860-949X

Conference

Conference	11th Annual Meeting of the Bulgarian Section of the Society for Industrial and Applied Mathematics, BGSIAM 2016
Country/Territory	Bulgaria
City	Sofia
Period	20/12/16 → 22/12/16

Bibliographical note

Publisher Copyright:
© 2018, Springer International Publishing AG.

Access to Document

10.1007/978-3-319-65530-7_2

Cite this

Ben-Artzi, M., Croisille, J. P., & Fishelov, D. (2018). An Embedded Compact Scheme for Biharmonic Problems in Irregular Domains. In M. Todorov, I. Georgiev, K. Georgiev, & I. Georgiev (Eds.), Advanced Computing in Industrial Mathematics - 11th Annual Meeting of the Bulgarian Section of SIAM, Revised Selected Papers (pp. 11-23). (Studies in Computational Intelligence; Vol. 728). Springer Verlag. https://doi.org/10.1007/978-3-319-65530-7_2

Ben-Artzi, Matania ; Croisille, Jean Pierre ; Fishelov, Dalia. / An Embedded Compact Scheme for Biharmonic Problems in Irregular Domains. Advanced Computing in Industrial Mathematics - 11th Annual Meeting of the Bulgarian Section of SIAM, Revised Selected Papers. editor / Michail Todorov ; Ivan Georgiev ; Krassimir Georgiev ; Ivan Georgiev. Springer Verlag, 2018. pp. 11-23 (Studies in Computational Intelligence).

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abstract = "In Ben-Artzi et al. (SIAM J Numer Anal 47:3087–3108 (2009), [1]) a Cartesian embedded finite difference scheme for biharmonic problems has been introduced. The design of the scheme relies on a 19-dimensional polynomial space. In this paper, we show how to simplify the implementation by introducing a directional decomposition of this space. The boundary is handled via a level-set approach. Numerical results for non convex domains demonstrate the fourth order accuracy of the scheme.",

author = "Matania Ben-Artzi and Croisille, \{Jean Pierre\} and Dalia Fishelov",

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Ben-Artzi, M, Croisille, JP & Fishelov, D 2018, An Embedded Compact Scheme for Biharmonic Problems in Irregular Domains. in M Todorov, I Georgiev, K Georgiev & I Georgiev (eds), Advanced Computing in Industrial Mathematics - 11th Annual Meeting of the Bulgarian Section of SIAM, Revised Selected Papers. Studies in Computational Intelligence, vol. 728, Springer Verlag, pp. 11-23, 11th Annual Meeting of the Bulgarian Section of the Society for Industrial and Applied Mathematics, BGSIAM 2016, Sofia, Bulgaria, 20/12/16. https://doi.org/10.1007/978-3-319-65530-7_2

An Embedded Compact Scheme for Biharmonic Problems in Irregular Domains. / Ben-Artzi, Matania; Croisille, Jean Pierre; Fishelov, Dalia.
Advanced Computing in Industrial Mathematics - 11th Annual Meeting of the Bulgarian Section of SIAM, Revised Selected Papers. ed. / Michail Todorov; Ivan Georgiev; Krassimir Georgiev; Ivan Georgiev. Springer Verlag, 2018. p. 11-23 (Studies in Computational Intelligence; Vol. 728).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Ben-Artzi M, Croisille JP, Fishelov D. An Embedded Compact Scheme for Biharmonic Problems in Irregular Domains. In Todorov M, Georgiev I, Georgiev K, Georgiev I, editors, Advanced Computing in Industrial Mathematics - 11th Annual Meeting of the Bulgarian Section of SIAM, Revised Selected Papers. Springer Verlag. 2018. p. 11-23. (Studies in Computational Intelligence). doi: 10.1007/978-3-319-65530-7_2

An Embedded Compact Scheme for Biharmonic Problems in Irregular Domains

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