Premium
Multigrid solution of the Poisson—Boltzmann equation
Author(s) -
Holst Michael,
Saied Faisal
Publication year - 1993
Publication title -
journal of computational chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.907
H-Index - 188
eISSN - 1096-987X
pISSN - 0192-8651
DOI - 10.1002/jcc.540140114
Subject(s) - multigrid method , discretization , poisson's equation , relaxation (psychology) , boltzmann equation , mathematics , poisson–boltzmann equation , finite element method , computer science , partial differential equation , computational science , mathematical analysis , physics , thermodynamics , psychology , social psychology , ion , quantum mechanics
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.