Department of Computer Science, University of Illinois Urbana Champaign
The nonlinear Poisson-Boltzmann equation (NLPBE) of Bio-Physics models the electrostatic field of a molecule in an ionic solution. It is a continuum model, that leads to a three-dimensional, nonlinear elliptic pde, with discontinuous coefficients. We show that multiscale solvers can be very effective for the solution of this problem. In particular, we develop multigrid-based Newton iterations for the NLPBE. The performance of these solvers for some molecules is compared to other algorithms, and the computed solution is compared to some experimental results. Visualization results and some performance data for parallel implementations of these methods will be presented.