Inexact IETI-DP for Conforming Isogeometric Multi-Patch Discretizations

Rainer Schneckenleitner; Stefan Takacs

doi:10.1007/978-3-031-20432-6_26

Inexact IETI-DP for Conforming Isogeometric Multi-Patch Discretizations

Rainer Schneckenleitner^*
, Stefan Takacs

^*Corresponding author for this work

Electrical Engineering

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

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Abstract

In this paper, we investigate Dual-Primal Isogeometric Tearing and Interconnecting (IETI-DP) methods for conforming Galerkin discretizations on multi-patch computational domains with inexact subdomain solvers. Recently, the authors have proven a condition number estimate for a IETI-DP solver that is explicit, among other parameters, in the grid size and the spline degree. The analysis assumes that the local subproblems are solved exactly, e.g., using a direct solver. In the present paper, we change the method in order to allow inexact solvers for the local subproblems, namely solvers based on the fast diagonalization method. This gives a faster overall solver, maintaining the same explicit condition number bound.

Original language	English
Title of host publication	Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2020+1 - Selected Papers from the ICOSAHOM Conference 2021
Editors	Jens M. Melenk, Ilaria Perugia, Joachim Schöberl, Christoph Schwab
Publisher	Springer
Pages	399-410
Number of pages	12
ISBN (Electronic)	9783031204326
ISBN (Print)	9783031204319
DOIs	https://doi.org/10.1007/978-3-031-20432-6_26
Publication status	Published - 2023
Publication type	A4 Article in conference proceedings
Event	International Conference on Spectral and High Order Methods - Vienna, Austria Duration: 12 Jul 2021 → 16 Jul 2021

Publication series

Name	Lecture Notes in Computational Science and Engineering
Volume	137
ISSN (Print)	1439-7358
ISSN (Electronic)	2197-7100

Conference

Conference	International Conference on Spectral and High Order Methods
Country/Territory	Austria
City	Vienna
Period	12/07/21 → 16/07/21

Funding

The first author was supported by the Austrian Science Fund (FWF): S11703 and W1214-04. Also, the second author has received support from the Austrian Science Fund (FWF): P31048.

Funders	Funder number
The Austrian Science Fund	W1214-04, S11703, P31048

Publication forum classification

Publication forum level 1

ASJC Scopus subject areas

Modelling and Simulation
General Engineering
Discrete Mathematics and Combinatorics
Control and Optimization
Computational Mathematics

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10.1007/978-3-031-20432-6_26

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Schneckenleitner, R., & Takacs, S. (2023). Inexact IETI-DP for Conforming Isogeometric Multi-Patch Discretizations. In J. M. Melenk, I. Perugia, J. Schöberl, & C. Schwab (Eds.), Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2020+1 - Selected Papers from the ICOSAHOM Conference 2021 (pp. 399-410). (Lecture Notes in Computational Science and Engineering; Vol. 137). Springer. https://doi.org/10.1007/978-3-031-20432-6_26

Schneckenleitner, Rainer ; Takacs, Stefan. / Inexact IETI-DP for Conforming Isogeometric Multi-Patch Discretizations. Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2020+1 - Selected Papers from the ICOSAHOM Conference 2021. editor / Jens M. Melenk ; Ilaria Perugia ; Joachim Schöberl ; Christoph Schwab. Springer, 2023. pp. 399-410 (Lecture Notes in Computational Science and Engineering).

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title = "Inexact IETI-DP for Conforming Isogeometric Multi-Patch Discretizations",

abstract = "In this paper, we investigate Dual-Primal Isogeometric Tearing and Interconnecting (IETI-DP) methods for conforming Galerkin discretizations on multi-patch computational domains with inexact subdomain solvers. Recently, the authors have proven a condition number estimate for a IETI-DP solver that is explicit, among other parameters, in the grid size and the spline degree. The analysis assumes that the local subproblems are solved exactly, e.g., using a direct solver. In the present paper, we change the method in order to allow inexact solvers for the local subproblems, namely solvers based on the fast diagonalization method. This gives a faster overall solver, maintaining the same explicit condition number bound.",

author = "Rainer Schneckenleitner and Stefan Takacs",

note = "Publisher Copyright: {\textcopyright} 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.; International Conference on Spectral and High Order Methods ; Conference date: 12-07-2021 Through 16-07-2021",

year = "2023",

doi = "10.1007/978-3-031-20432-6\_26",

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

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editor = "Melenk, \{Jens M.\} and Ilaria Perugia and Joachim Sch{\"o}berl and Christoph Schwab",

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Schneckenleitner, R & Takacs, S 2023, Inexact IETI-DP for Conforming Isogeometric Multi-Patch Discretizations. in JM Melenk, I Perugia, J Schöberl & C Schwab (eds), Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2020+1 - Selected Papers from the ICOSAHOM Conference 2021. Lecture Notes in Computational Science and Engineering, vol. 137, Springer, pp. 399-410, International Conference on Spectral and High Order Methods, Vienna, Austria, 12/07/21. https://doi.org/10.1007/978-3-031-20432-6_26

Inexact IETI-DP for Conforming Isogeometric Multi-Patch Discretizations. / Schneckenleitner, Rainer; Takacs, Stefan.
Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2020+1 - Selected Papers from the ICOSAHOM Conference 2021. ed. / Jens M. Melenk; Ilaria Perugia; Joachim Schöberl; Christoph Schwab. Springer, 2023. p. 399-410 (Lecture Notes in Computational Science and Engineering; Vol. 137).

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

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AU - Schneckenleitner, Rainer

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PY - 2023

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N2 - In this paper, we investigate Dual-Primal Isogeometric Tearing and Interconnecting (IETI-DP) methods for conforming Galerkin discretizations on multi-patch computational domains with inexact subdomain solvers. Recently, the authors have proven a condition number estimate for a IETI-DP solver that is explicit, among other parameters, in the grid size and the spline degree. The analysis assumes that the local subproblems are solved exactly, e.g., using a direct solver. In the present paper, we change the method in order to allow inexact solvers for the local subproblems, namely solvers based on the fast diagonalization method. This gives a faster overall solver, maintaining the same explicit condition number bound.

AB - In this paper, we investigate Dual-Primal Isogeometric Tearing and Interconnecting (IETI-DP) methods for conforming Galerkin discretizations on multi-patch computational domains with inexact subdomain solvers. Recently, the authors have proven a condition number estimate for a IETI-DP solver that is explicit, among other parameters, in the grid size and the spline degree. The analysis assumes that the local subproblems are solved exactly, e.g., using a direct solver. In the present paper, we change the method in order to allow inexact solvers for the local subproblems, namely solvers based on the fast diagonalization method. This gives a faster overall solver, maintaining the same explicit condition number bound.

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DO - 10.1007/978-3-031-20432-6_26

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BT - Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2020+1 - Selected Papers from the ICOSAHOM Conference 2021

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Schneckenleitner R, Takacs S. Inexact IETI-DP for Conforming Isogeometric Multi-Patch Discretizations. In Melenk JM, Perugia I, Schöberl J, Schwab C, editors, Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2020+1 - Selected Papers from the ICOSAHOM Conference 2021. Springer. 2023. p. 399-410. (Lecture Notes in Computational Science and Engineering). doi: 10.1007/978-3-031-20432-6_26

Inexact IETI-DP for Conforming Isogeometric Multi-Patch Discretizations

Abstract

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