The Poisson-Boltzmann equation is a partial differential equation that describes the electrostatic behavior of molecules in ionic solutions. Significant efforts have been devoted to accurate and efficient computation for solving this equation. In this paper, we developed a boundary element framework based on the linear time fast multipole method for solving the linearized PoissonBoltzmann equat...

Abstract: Numerically solving the Poisson-Boltzmann equation is a challenging task due to the existence of the dielectric interface, singular partial charges representing the biomolecule, discontinuity of the electrostatic field, infinite simulation domains, etc. Boundary integral formulation of the Poisson-Boltzmann equation can circumvent these numerical challenges and meanwhile conveniently ...

An isomorphism of the Lie algebras L11 admissible by the full Boltzmann kinetic equation with an arbitrary differential cross section and by the Euler gas dynamics system of equations with a general state equation is set up. The similarity is also proved between extended algebras L12 admissible by the same equations for specified power-like intermolecular potentials and for polytropic gas. This...

This paper presents a new finite-volume discretization of a generalised Lattice Boltzmann equation (LBE) on unstructured grids. This equation is the continuum LBE, with the addition of a second order time derivative term (memory), and is derived from a second-order differential form of the semi-discrete Boltzmann equation in its implicit form. The new scheme, named unstructured lattice Boltzman...