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Stephen D. Bond

Citation:

Burak Aksoylu, Stephen D. Bond, Eric C. Cyr and Michael J. Holst, Goal-Oriented Adaptivity and Multilevel Preconditioning for the Poisson-Boltzmann Equation, Journal of Scientific Computing 52:1 (2012) 202-225.

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 specific marking strategy, combined with goal-oriented refinement, compares favorably to adaptive methods using the 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 BPX preconditioners.

Full Text:

DOI: 10.1007/s10915-011-9539-6

Preprint:

Goal-Oriented Adaptivity and Multilevel Preconditioning for the Poisson-Boltzmann Equation (952K, PDF)

Bibtex:
@article{ABCH2012,
  author  = {Burak Aksoylu and Stephen D. Bond and Eric C. Cyr and Michael J.
             Holst},
  title   = {Goal-Oriented Adaptivity and Multilevel Preconditioning for the
             {P}oisson-{B}oltzmann Equation},
  journal = {Journal of Scientific Computing},
  volume  = 52,
  number  = 1,
  year    = 2012,
  pages   = {202--225},
  doi     = {10.1007/s10915-011-9539-6},
  note    = {SAND Number 2011-4803 J}
}

Stephen Bond