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Probabilistic interpretation and random walk on spheres algorithms for the Poisson-Boltzmann equation in molecular dynamics. (English) Zbl 1204.82020
This paper firstly derives a new probabilistic interpretation for a class of divergence-form operators, and then uses it to construct Monte Carlo methods for the linearized Poisson-Boltzmann equation in molecular dynamics. The Feynman-Kac formula is extended to the solution of a class of PDE involving divergence-form operators, and the proposed Monte Carlo algorithms are based on random walks on spheres.

82B41 Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics
35Q60 PDEs in connection with optics and electromagnetic theory
92C40 Biochemistry, molecular biology
60J60 Diffusion processes
65C05 Monte Carlo methods
65C20 Probabilistic models, generic numerical methods in probability and statistics
68U20 Simulation (MSC2010)
82B80 Numerical methods in equilibrium statistical mechanics (MSC2010)
Full Text: DOI EuDML
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