Multigrid solution of the Poisson—Boltzmann equation

TLDR

The study presents a multigrid method for numerically solving the linearized Poisson–Boltzmann equation in molecular biophysics. The equation is discretized by finite volume and solved with multigrid techniques derived from reactor‑physics interface problems, and its performance is evaluated on multiple computer architectures against CG, ICCG, vectorized ICCG, MICCG, and optimally relaxed SOR. The multigrid method outperforms preconditioned CG and optimal SOR, with its advantage increasing with problem size. © 1993 John Wiley & Sons, Inc.

Abstract

Abstract A multigrid method is presented for the numerical solution of the linearized Poisson–Boltzmann equation arising in molecular biophysics. The equation is discretized with the finite volume method, and the numerical solution of the discrete equations is accomplished with multiple grid techniques originally developed for twodimensional interface problems occurring in reactor physics. A detailed analysis of the resulting method is presented for several computer architectures, including comparisons to diagonally scaled CG, ICCG, vectorized ICCG and MICCG, and to SOR provided with an optimal relaxation parameter. Our results indicate that the multigrid method is superior to the preconditioned CG methods and SOR and that the advantage of multigrid grows with the problem size. © 1993 John Wiley & Sons, Inc.