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Goal-oriented adaptivity and multilevel preconditioning for the Poisson-Boltzmann equation. (English) Zbl 1263.78011

An adaptive multilevel finite element method for the Poisson-Boltzmann equation (PBE) is discussed. Especially, the authors propose goal-oriented a posteriori error indicators and a problem-specific marking strategy, which are applied to numerically solve the PBE. They also combine Bramble-Pasciak-Xu (BPX)-type multilevel preconditioners with the proposed goal-oriented adaptive algorithm. Numerical experiments are also given, which demonstrate the efficiency of the proposed method.

MSC:

78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory
35Q20 Boltzmann equations
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
65F08 Preconditioners for iterative methods
78A35 Motion of charged particles
78A30 Electro- and magnetostatics
65N15 Error bounds for boundary value problems involving PDEs

Software:

SG; PDB2PQR; CHARMM; APBS
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

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