An inexact Dual-Primal Isogeometric Tearing and Interconnecting Method for continuous Galerkin discretizations

DI Rainer Schneckenleitner

June 8, 2021, 4:15 p.m. ZOOM

Recently, the authors have proven for the first time a condition number estimate for a dual-primal isogeometric tearing and interconnecting (IETI-DP) method for the Poisson problem that is explicit not only in the grid size and the subdomain diameter, but also in the spline degree. In the analysis of the IETI-DP method and the numerical experiments, the authors only have considered exact solvers for the local subproblems. In this talk, we construct and analyze a IETI-DP solver that allows the incorporation of inexact local solvers.
We use the fast diagonalization (FD) method as inexact solvers for the arising local subproblems. We show that the condition number of the proposed IETI-DP method does not deteriorate in this case. The numerical experiments show that the new solver with FD as inexact local solvers is significantly faster than the IETI-DP methods with sparse direct local solvers. In addition, the use of FD requires less memory compared to the use of sparse direct local solvers.

References
[1] Sangalli, G. and Tani, M. Isogeometric Preconditioners Based on Fast Solvers for the Sylvester Equation. SIAM J. Sci. Comput. vol. 38(6), pp. A3644-A3671, 2016.
[2] Schneckenleitner, R. and Takacs, S. Condition number bounds for IETI-DP methods that are explicit in h and p. Math. Models Methods Appl. Sci. vol. 30(11), pp. 2067-2103, 2020.