Application of an iterative Golub-Kahan algorithm to structural mechanics problems with multi-point constraints
Open Access
- 17 November 2020
- journal article
- Published by Springer Science and Business Media LLC in Advanced Modeling and Simulation in Engineering Sciences
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.Keywords
Funding Information
- Bpifrance (P113165-2621644/DOS0022362/DOS0022360)
This publication has 15 references indexed in Scilit:
- Generalized Golub--Kahan Bidiagonalization and Stopping CriteriaSIAM Journal on Matrix Analysis and Applications, 2013
- On the solution of multi-point constraints – Application to FE analysis of reinforced concrete structuresComputers & Structures, 2009
- Numerical solution of saddle point problemsActa Numerica, 2005
- Algebraic elimination of slide surface constraints in implicit structural analysisInternational Journal for Numerical Methods in Engineering, 2003
- On Solving Block-Structured Indefinite Linear SystemsSIAM Journal on Scientific Computing, 2003
- Efficient iterative solution of constrained finite element analysesComputer Methods in Applied Mechanics and Engineering, 1998
- Efficient Management of Parallelism in Object-Oriented Numerical Software LibrariesPublished by Springer Science and Business Media LLC ,1997
- ACM Transactions on Mathematical Software, 1982
- An algorithm for multipoint constraints in finite element analysisInternational Journal for Numerical Methods in Engineering, 1979
- Calculating the Singular Values and Pseudo-Inverse of a MatrixJournal of the Society for Industrial and Applied Mathematics Series B Numerical Analysis, 1965