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

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

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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 Swivels 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 Gloves be difficult for iterative solvers.