5 papers
Two-level additive Schwarz preconditioners for reduced integration methods
Filipe Cumaru, Alexander Heinlein, Joachim Schöberl
Incompressible fluid flow problems appear frequently in different applications. The discretization of such problems may result in large and ill-conditioned systems of linear equati…
Sharpened PCG Iteration Bound for High-Contrast Heterogeneous Scalar Elliptic PDEs
Philip Soliman, Filipe Cumaru, Alexander Heinlein
A new iteration bound for the preconditioned conjugate gradient (PCG) method is presented that more accurately captures convergence for systems with clustered eigenspectra, where t…
Monolithic and Block Overlapping Schwarz Preconditioners for the Incompressible Navier-Stokes Equations
Alexander Heinlein, Axel Klawonn, Jascha Knepper +1
Monolithic preconditioners applied to the linear systems arising during the solution of the discretized incompressible Navier-Stokes equations are typically more robust than precon…
Nonlinear Two-Level Schwarz Methods: A Parallel Implementation in FROSch
Alexander Heinlein, Kyrill Ho, Axel Klawonn +1
Owing to the ability of nonlinear domain decomposition methods to improve the nonlinear convergence behavior of Newton's method, they have experienced a rise in popularity recently…
A computational study of algebraic coarse spaces for two-level overlapping additive Schwarz preconditioners
Filipe A. C. S. Alves, Alexander Heinlein, Hadi Hajibeygi
The two-level overlapping additive Schwarz method offers a robust and scalable preconditioner for various linear systems resulting from elliptic problems. One of the key to these p…