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

Date: 13/02/2023 11:00
Place: Department of Mathematics meeting room (B-365) - Faculty of Civil Engineering CTU

We would like to invite all SIAM members and friends to a lecture on Domain decomposition methods for highly-heterogeneous problems–Robust coarse spaces and nonlinear preconditioning given by Alexander Heinlein from Delft University of Technology (TU Delft).

The event will take place in the meeting room of Department of Mechanics (B-366) on Monday, 13th February, from 11:00, followed by a discussion. 

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.