Paper Info
Title
Goal-Oriented Adaptivity and Multilevel Preconditioning for the Poisson-Boltzmann Equation
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.
Year
DOI
Venue
2012
10.1007/s10915-011-9539-6
J. Sci. Comput.
Keywords
Field
DocType
poisson-boltzmann equation,goal-oriented error indicator,multilevel preconditioning,energy-based error indicator,goal-oriented indicator,superior refinement algorithm,adaptive refinement algorithm,solvation free energy,adaptive mesh refinement,classical multigrid method,goal-oriented refinement,goal-oriented adaptivity,numerical analysis,free energy,poisson boltzmann equation,goal orientation,multigrid method
Convergence (routing),Poisson–Boltzmann equation,Mathematical optimization,Linear form,Generalization,Adaptive mesh refinement,Solvation,Mathematics,Multigrid method,Computational complexity theory
Journal
Volume
Issue
ISSN
52
1
1573-7691
Citations 
PageRank 
References 
2
0.41
22
Authors
4
Name
Order
Citations
PageRank
Burak Aksoylu1819.76
Stephen D. Bond2275.10
Eric C. Cyr3518.66
Michael Holst4607.84