Bosy, M; Montardini, M; Sangalli, G; Tani, M; (2020) A domain decomposition method for Isogeometric multi-patch problems with inexact local solvers. Computers and Mathematics with Applications , 80 (11) pp. 2604-2621. 10.1016/j.camwa.2020.08.024.

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Abstract

In Isogeometric Analysis, the computational domain is often described as multi-patch, where each patch is given by a tensor product spline/NURBS parametrization. In this work we propose a FETI-like solver where local inexact solvers exploit the tensor product structure at the patch level. To this purpose, we extend to the isogeometric framework the so-called All-Floating variant of FETI, that allows us to use the Fast Diagonalization method at the patch level. We construct then a preconditioner for the whole system and prove its quasi-robustness with respect to the local mesh-size h and patch-size H: precisely the condition number of the preconditioned system is bounded by the square of the logarithm of H∕h. Our numerical tests confirm the theory and also show a favourable dependence of the computational cost of the method from the spline degree p.

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