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A hybrid solver of size modified Poisson-Boltzmann equation by domain decomposition, finite element, and finite difference. (English) Zbl 1480.65348

Summary: The size-modified Poisson-Boltzmann equation (SMPBE) is one important variant of the popular dielectric model, the Poisson-Boltzmann equation (PBE), to reflect ionic size effects in the prediction of electrostatics for a biomolecule in an ionic solvent. In this paper, a new SMPBE hybrid solver is developed using a solution decomposition, Schwartz’s overlapped domain decomposition, finite element, and finite difference. It is then programmed as a software package in C, Fortran, and Phython based on the state-of-the-art finite element library DOLFIN from the FEniCS project. This software package is well validated on a Born ball model with analytical solution and a dipole model with known physical properties. Numerical results on six proteins with different net charges demonstrate its high performance. Finally, this new SMPBE hybrid solver is shown to be numerically stable and convergent in the calculation of electrostatic solvation free energy for 216 biomolecules and binding free energy for a DNA-drug complex.

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N06 Finite difference methods for boundary value problems involving PDEs
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
65Y15 Packaged methods for numerical algorithms
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References:

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