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Adaptive numerical components for PDE‐based simulations
Author(s) -
Norris Boyana,
McInnes Lois Curfman,
Bhowmick Sanjukta,
Li Li
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700687
Subject(s) - solver , nonlinear system , partial differential equation , computer science , linear system , mathematical optimization , heuristics , mathematics , newton's method , system of linear equations , mathematical analysis , physics , quantum mechanics
Numerical simulations based on nonlinear partial differential equations (PDEs) using Newton‐based methods require the solution of large, sparse linear systems of equations at each nonlinear iteration. Typically in large‐scale parallel simulations such linear systems are solved by using preconditioned Krylov methods. In many cases, especially in time‐dependent problems, the attributes of the linear systems can change throughout the stimulation, potentially leading to varying times for solving the linear systems during different nonlinear iterations. We present an approach to characterizing the nonlinear and linear system solution and using the resulting application performance information to dynamically select linear solver methods, with the goal of reducing the total time to solution. We discuss the effect of these adaptive heuristics on fluid dynamics and radiation transport codes. We also introduce general component infrastructure to support dynamic algorithm selection and adaptation in applications involving the solution of nonlinear PDEs. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)