Please use this identifier to cite or link to this item:
https://hdl.handle.net/20.500.11851/6783
Title: | Goal-Oriented Adaptivity and Multilevel Preconditioning for the Poisson-Boltzmann Equation | Authors: | Aksoylu, Burak Bond, Stephen D. Cyr, Eric C. Holst, Michael |
Keywords: | Poisson-Boltzmann equation Adaptive finite element methods Multilevel preconditioning Goal-oriented a posteriori error estimation Solvation free energy Electrostatics |
Publisher: | Springer/Plenum Publishers | Abstract: | In this article, we develop goal-oriented error indicators to drive adaptive refinement algorithms for the Poisson-Boltzmann equation. Empirical results for the solvation free energy linear functional demonstrate that goal-oriented indicators are not sufficient on their own to lead to a superior refinement algorithm. To remedy this, we propose a problem-specific marking strategy using the solvation free energy computed from the solution of the linear regularized Poisson-Boltzmann equation. The convergence of the solvation free energy using this marking strategy, combined with goal-oriented refinement, compares favorably to adaptive methods using an energy-based error indicator. Due to the use of adaptive mesh refinement, it is critical to use multilevel preconditioning in order to maintain optimal computational complexity. We use variants of the classical multigrid method, which can be viewed as generalizations of the hierarchical basis multigrid and Bramble-Pasciak-Xu (BPX) preconditioners. | URI: | https://doi.org/10.1007/s10915-011-9539-6 https://hdl.handle.net/20.500.11851/6783 |
ISSN: | 0885-7474 1573-7691 |
Appears in Collections: | Matematik Bölümü / Department of Mathematics Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection |
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