Communications in Mathematical Sciences

Volume 13 (2015)

Number 2

A new linear Poisson-Boltzmann equation and finite element solver by solution decomposition approach

Pages: 315 – 325



Jiao Li (School of Mathematics and Computer Science, Changsha University of Science and Technology, Changsha, Hunan, China)

Dexuan Xie (Department of Mathematical Sciences, University of Wisconsin, Milwaukee, Wisc., U.S.A.)


The linear Poisson-Boltzmann equation (LPBE) is one well-known implicit solvent continuum model for computing the electrostatic potential of biomolecules in ionic solvent. To overcome its singular difficulty caused by Dirac delta distributions of point charges and to further improve its solution accuracy, we develop in this paper a new scheme for solving the current LPBE model, a new LPBE model, and a new LPBE finite element program package based on our previously proposed PBE solution decomposition. Numerical tests on biomolecules and a nonlinear Born ball model with an analytical solution validate the new LPBE solution decomposition schemes, demonstrate the effectiveness and efficiency of the new program package, and confirm that the new LPBE model can significantly improve the solution accuracy of the current LPBE model.


Poisson-Boltzmann equation, implicit solvent, biomolecular electrostatics, finite elementmethod

2010 Mathematics Subject Classification

65K10, 65N30, 92-08

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