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.