Adaptive Coarse Space Selection in the BDDC and the FETI-DP Iterative Substructuring Methods: Optimal Face Degrees of Freedom
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2007
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Mandel J., Sousedík B. (2007) Adaptive Coarse Space Selection in the BDDC and the FETI-DP Iterative Substructuring Methods: Optimal Face Degrees of Freedom. In: Widlund O.B., Keyes D.E. (eds) Domain Decomposition Methods in Science and Engineering XVI. Lecture Notes in Computational Science and Engineering, vol 55. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-34469-8_52
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Abstract
We propose adaptive selection of the coarse space of the BDDC and
FETI-DP iterative substructuring methods by adding coarse degrees of freedom
(dofs) on faces between substructures constructed using eigenvectors associated with
the faces. Provably the minimal number of coarse dofs on the faces is added to
decrease a heuristic indicator of the condition number under a target value specified
a priori. It is assumed that corner dofs are already sufficient to prevent relative
rigid body motions of any two substructures with a common face. It is shown
numerically on a 2D elasticity problem that the indicator is reasonably close to
the actual condition number and that the method can find automatically the hard
part of the problem and concentrate the computational work there to achieve the
target value for the condition number and good convergence of the iterations, at a
modest cost.