A domain decomposition method for Isogeometric multi-patch problems with inexact local solvers. (1st December 2020)

• Record Type: Journal Article
• Authors: Bosy, Michał; Montardini, Monica; Sangalli, Giancarlo; Tani, Mattia
• Is Part Of: Computers & mathematics with applications. Volume 80:issue 11(2020)
• Page Start: 2604
• Page End: 2621
• Publication Date: 2020-12-01
• Subjects: Isogeometric Analysis -- Domain decomposition -- FETI -- IETI -- Preconditioners -- Fast Diagonalization; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2020.08.024
• Languages: English
• ISSNs: 0898-1221

Abstract

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 .