| Summary: | The electrostatic potential in the neighborhood of a biomolecule can be computed thanks
to the non-linear divergence-form elliptic Poisson-Boltzmann PDE. Dedicated Monte-Carlo
methods have been developed to solve its linearized version (see e.g. [7], [27]). These
algorithms combine walk on spheres techniques and appropriate
replacements at the boundary of the molecule. In the first part of this article we compare
recent replacement methods for this linearized equation on real size biomolecules, that
also require efficient computational geometry algorithms. We compare our results with the
deterministic solver APBS. In the second part, we prove a new probabilistic interpretation
of the nonlinear Poisson-Boltzmann PDE. A Monte Carlo algorithm is also derived and tested
on a simple test case.
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