Department of Mechanics: Seminar: Alexander Heinlein 2023

Domain decomposition methods for highly-heterogeneous problems–Robust coarse spaces and nonlinear preconditioning

Alexander Heinlein TU Delft, the Netherlands

13 February 2023, 10:00-11:00 CET, Room B-366 @ Thákurova 7, 166 29 Prague 6

Abstract

Two-level domain decomposition methods, such as two-level Schwarz, finite element tearing and interconnecting - dual primal (FETI-DP), or balancing domain decomposition by constraints (BDDC) methods, are scalable for a large class of homogeneous problems. However, in the presence of highly-heterogeneous coefficients, convergence generally deteriorates. If the coarse space is enhanced by adapted coarse basis functions, robustness can be regained.

Similar observations can be made for highly-heterogeneous nonlinear problems, where both the linear and the nonlinear convergence maybe affected; in this context, a combination of nonlinear domain decomposition methods and robust coarse spaces can recover good linear and nonlinear solver performance.

In this talk, preconditioning techniques for highly-heterogeneous linear and nonlinear problems will be discussed and numerical results for various problems will be reported; the focus is on Schwarz domain decomposition methods, but many approaches can be - with small modifications - applied to other domain decomposition methods as well.