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Inexact IETI-DP for Conforming Isogeometric Multi-Patch Discretizations

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Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2020+1

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 137))

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.

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Notes

  1. 1.

    https://github.com/gismo/gismo.

  2. 2.

    https://www.ricam.oeaw.ac.at/hpc/.

  3. 3.

    https://www.pardiso-project.org/.

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Acknowledgements

The first author was supported by the Austrian Science Fund (FWF): S117-03 and W1214-04. Also, the second author has received support from the Austrian Science Fund (FWF): P31048.

Author information

Authors and Affiliations

  1. Electrical Engineering Unit, Tampere University, Tampere, Finland

    Rainer Schneckenleitner

  2. Institute of Computational Mathematics, Johannes Kepler University Linz, Linz, Austria

    Stefan Takacs

Authors
  1. Rainer Schneckenleitner
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  2. Stefan Takacs
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Corresponding author

Correspondence to Rainer Schneckenleitner .

Editor information

Editors and Affiliations

  1. TU Wien, Wien, Austria

    Jens M. Melenk

  2. Universität Wien, Wien, Austria

    Ilaria Perugia

  3. TU Wien, Wien, Austria

    Joachim Schöberl

  4. ETH Zürich, Zürich, Switzerland

    Christoph Schwab

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Schneckenleitner, R., Takacs, S. (2023). Inexact IETI-DP for Conforming Isogeometric Multi-Patch Discretizations. In: Melenk, J.M., Perugia, I., Schöberl, J., Schwab, C. (eds) Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2020+1. Lecture Notes in Computational Science and Engineering, vol 137. Springer, Cham. https://doi.org/10.1007/978-3-031-20432-6_26

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