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Computational aspects of the weak micro‐periodicity saddle point problem
Author(s) -
Bharali Ritukesh,
Larsson Fredrik,
Jänicke Ralf
Publication year - 2021
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.202000259
Subject(s) - lagrange multiplier , saddle point , grid , saddle , degrees of freedom (physics and chemistry) , point (geometry) , mathematical optimization , mathematics , finite element method , computer science , geometry , physics , quantum mechanics , thermodynamics
The finite element implementation of the weak micro‐periodicity problem in computational homogenisation requires special preconditioning techniques owing to the saddle point formulation. The saddle point nature arises from enforcing periodicity constraints using Lagrange multipliers. This manuscript addresses the solution techniques and preconditioning options for the aforementioned problem in a monolithic setting. Furthermore, an alternative technique is proposed, based on a linear multi‐point constraints strategy. The latter approach eliminates the Lagrange multiplier Degrees of Freedom (DOFs), thereby preventing the break‐down of conventional incomplete LU (ILU) variants and multi‐grid method based preconditioners.