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Using Krylov-Schwarz methods in an adaptive mesh refinement environment. (English) Zbl 1246.65228

Plewa, Tomasz (ed.) et al., Adaptive mesh refinement – theory and applications. Proceedings of the Chicago workshop on adaptive mesh refinement methods, Chicago, IL, USA, September 3–5, 2003. Berlin: Springer (ISBN 3-540-21147-0/pbk). Lecture Notes in Computational Science and Engineering 41, 115-124 (2005).
Summary: Much of the previous work in adaptive mesh refinement (AMR) methods has concentrated on solving hyperbolic equations with explicit time-stepping. However, for many problems, either due to their physical nature (e.g., incompressible flows) or for performance reasons (semi-implicit and implicit numerical methods), it becomes necessary to solve global equations.
This paper focuses on the application and performance of well-established preconditioned Krylov-Schwarz solvers in an AMR context, using a Krylov-Schwarz method to accelerate convergence while exploiting the hierarchical structure of AMR grids for multi-level preconditioning using the fast adpative composite algorithm. We present an implementation that allows us to leverage the powerful supply of preconditioners and linear solvers from the PETSc library.
We apply this method to solve the three-dimensional Euler equations in the search for a finite-time singularity.
For the entire collection see [Zbl 1053.65002].

MSC:

65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs
76M25 Other numerical methods (fluid mechanics) (MSC2010)

Software:

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