The Development of an Object-Oriented Parallel Block Preconditioning Framework

Richard L. Muddle (), Jonathan W. Boyle (), Milan D. Mihajlović () and Matthias Heil ()
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Richard L. Muddle: Vilnius Gediminas Technical University and Institute of Mathematics and Informatics
Jonathan W. Boyle: Vilnius Gediminas Technical University and Institute of Mathematics and Informatics
Milan D. Mihajlović: Vilnius Gediminas Technical University and Institute of Mathematics and Informatics
Matthias Heil: Vilnius Gediminas Technical University and Institute of Mathematics and Informatics

A chapter in Parallel Scientific Computing and Optimization, 2009, pp 37-46 from Springer

Abstract: Abstract The finite-element-based solution of partial differential equations often requires the solution of large systems of linear equations. Krylov subspace methods are efficient solvers when combined with effective preconditioners. We consider block preconditioners that are applicable to problems that have different types of degree of freedom (e.g., velocity and pressure in a fluid simulation). We discuss the development of an object-oriented parallel block preconditioning framework within oomph-lib, the object-oriented, multi-physics, finite-element library, available as open-source software at http://www.oomph-lib.org. We demonstrate the performance of this framework for problems from non-linear elasticity, fluid mechanics, and fluid-structure interaction.

Date: 2009
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DOI: 10.1007/978-0-387-09707-7_3

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