Solution of the 3D nonlinear Poisson-Boltzmann equation is done by the multigrid methods on a detailed 3D finite element mesh of about 100,000 nodes. This was our first practical application of the 3D multigrid to biophysics problems inspired by Prof. P.Lazarev and Dr. V. Sivozhelezov.
It was done in 1990 using the IBM PC 386/20Mhz with 4Mb of memory. Typical CPU time was 20 mins. Same problem with standard methods required about 15 mins of CRAY X-MP (that was unavailable for us at that time). Now it will probably take 5 secs on Pentium 400 Mhz machine. The code was developed by S.Purtov and I.Petrenko at the Institute for High Energy Physics (IHEP) , Russia.
The only known to me our publication in English is:
S. Purtov, E. Chernyaev, P. Lazarev, I. Petrenko,
A. Fedoseyev, V.Sivozhelezov. Mathematical modelling of 3D protein
molecule potential in nonlinear media. Proc. of European Conf. Physics
en Herbe, Marseille, France, July 05-11, 1992, 8p.
Victor Sivozhelezov told me later that more detailed version of presentation has been submitted to Biophysics, and I do not have further details.
Picture of the computed 3D electrostatic field.
The potential surfaces of +1/2 kT and
-1/2 kT are plotted, k is a
Boltzmann constant, T is a temperature in Kelvin degrees ( 3D isosurface
plotting software was developed by E.Chernyaev during his stay at CERN
in 1992. He is also an author of xwpick
utility, that is widely used to capture and/or print X-window and available
in anyLINUX distribution):
to Alex homepage