A Short Note Comparing Multigrid and Domain Decomposition for Protein Modeling Equations

Abstract

We consider multigrid and domain decomposition methods for the numerical solution of electrostatics problems arising in biophysics. We compare multigrid methods designed for discontinuous coefficients with domain decomposition methods, including comparisons of standard multigrid methods, algebraic multigrid methods, additive and multiplicative Schwarz domain decomposition methods, and acceleration of multigrid and domain decomposition methods with conjugate gradient methods. As a test problem, we consider a linearization of the Poisson-Boltzmann equation, which describes the electrostatic potential of a large complex biomolecule lying in an ionic solvent