A Three-Level Extension for Fast and Robust Overlapping Schwarz (FROSch) Preconditioners with Reduced Dimensional Coarse Space

The Fast and Robust Overlapping Schwarz framework [7, 8], which is part of the Trilinos Software library [18], contains a parallel implementation of the generalized Dryja–Smith–Widlund (GDSW) preconditioner.

Predicting the Geometric Location of Critical Edges in Adaptive GDSW Overlapping Domain Decomposition Methods Using Deep Learning

For complex model problems with coefficient or material distributions with large jumps along or across the domain decomposition interface, the convergence rate of classic domain decomposition methods for scalar elliptic problems usually deteriorates. In particular, the classic condition number bounds [1, 12] will depend on the contrast of the...

Inexact Subdomain Solves Using Deflated GMRES for Helmholtz Problems

In recent years, domain decomposition based preconditioners have become popular tools to solve the Helmholtz equation. Notorious for causing a variety of convergence issues, the Helmholtz equation remains a challenging PDE to solve numerically. Even for simple model problems, the resulting linear system after discretisation becomes indefinite...