Application of an iterative Golub-Kahan algorithm to structural mechanics problems with multi-point constraints

Kruse C, Darrigrand V, Tardieu N, Arioli M, Rüde U (2020)

Publication Type: Journal article

Publication year: 2020

Journal

Advanced Modeling and Simulation in Engineering Sciences Springer Open

Book Volume: 7

Article Number: 45

Journal Issue: 1

DOI: 10.1186/s40323-020-00181-2

Abstract

Kinematic relationships between degrees of freedom, also named multi-point constraints, are frequently used in structural mechanics. In this paper, the Craig variant of the Golub-Kahan bidiagonalization algorithm is used as an iterative method to solve the arising linear system with a saddle point structure. The condition number of the preconditioned operator is shown to be close to unity and independent of the mesh size. This property is proved theoretically and illustrated on a sequence of test problems of increasing complexity, including concrete structures enforced with pretension cables and the coupled finite element model of a reactor containment building. The Golub-Kahan algorithm converges in only a small number of steps for all considered test problems and discretization sizes. Furthermore, it is robust in practical cases that are otherwise considered to be difficult for iterative solvers.

Authors with CRIS profile

Ulrich Rüde Lehrstuhl für Informatik 10 (Systemsimulation)

Involved external institutions

University of Bari Aldo Moro / Università degli Studi di Bari Aldo Moro IT Italy (IT) Centre Européen de Recherche et de Formation Avancée en Calcul Scientifique (CERFACS) FR France (FR) École Polytechnique - Université Paris-Saclay FR France (FR)

How to cite

APA:

Kruse, C., Darrigrand, V., Tardieu, N., Arioli, M., & Rüde, U. (2020). Application of an iterative Golub-Kahan algorithm to structural mechanics problems with multi-point constraints. Advanced Modeling and Simulation in Engineering Sciences, 7(1). https://dx.doi.org/10.1186/s40323-020-00181-2

MLA:

Kruse, Carola, et al. "Application of an iterative Golub-Kahan algorithm to structural mechanics problems with multi-point constraints." Advanced Modeling and Simulation in Engineering Sciences 7.1 (2020).

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