Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Distributed Schur Complement Techniques for General Sparse Linear Systems
SIAM Journal on Scientific Computing
A new version of the fast multipole method for screened Coulomb interactions in three dimensions
Journal of Computational Physics
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Using the parallel algebraic recursive multilevel solver in modern physical applications
Future Generation Computer Systems - Special issue: Selected numerical algorithms
A class of difference schemes with flexible local approximation
Journal of Computational Physics
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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.