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
Issue Date: 2012
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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