Parallel Solvers for Flexible Approximation Schemes in Multiparticle Simulation

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New finite difference schemes with flexible local approximation are applied to screened electrostatic interactions of spherical colloidal particles governed by the Poisson-Boltzmann equation. Local analytical approximations of the solution are incorporated directly into the scheme and yield high approximation accuracy even on simple and relatively coarse Cartesian grids. Several parallel iterative solution techniques have been tested with an emphasis on suitable parallel preconditioning for the nonsymmetric system matrix. In particular, flexible GMRES preconditioned with the distributed Schur Complement exhibits good solution time and scales well when the number of particles, grid nodes or processors increases.