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# mFES: A Robust Molecular Finite Element Solver for Electrostatic Energy Computations

journal contribution

posted on 2014-11-11, 00:00 authored by I. Sakalli, J. Schöberl, E. W. KnappWe
present a robust method for the calculation of electrostatic
potentials of large molecular systems using tetrahedral finite elements
(FE). Compared to the finite difference (FD) method using a regular
simple cubic grid to solve the Poisson equation, the FE method can
reach high accuracy and efficiency using an adaptive grid. Here, the
grid points can be adjusted and are placed directly on the molecular
surfaces to faithfully model surfaces and volumes. The grid point
density decreases rapidly toward the asymptotic boundary to reach
very large distances with just a few more grid points. A broad set
of tools are applied to make the grid more regular and thus provide
a more stable linear equation system, while reducing the number of
grid points without compromising accuracy. The latter reduces the
number of unknowns significantly and yields shorter solver execution
times. The accuracy is further enhanced by using second order polynomials
as shape functions. Generating the adaptive grid for a molecular system
is expensive, but it pays off, if the same molecular geometry is used
several times as is the case for p

*K*_{A}and redox potential computations of many charge variable groups in proteins. Application of the mFES method is also advantageous, if the molecular system is too large to reach sufficient accuracy when computing the electrostatic potential with conventional FD methods. The program mFES is free of charge and available at http://agknapp.chemie.fu-berlin.de/mfes.