A two-component Matched Interface and Boundary (MIB) regularization for charge singularity in implicit solvation

Weihua Geng Southern Methodist University, USA Shan Zhao University of Alabama, USA

Numerical Analysis and Scientific Computing Data Analysis, Bio-Statistics, Bio-Mathematics mathscidoc:2005.42001

Distinguished Paper Award in 2020

Journal of Computational Physics, 351, 25-39, 2017
We present a new Matched Interface and Boundary (MIB) regularization method for treating charge singularity in solvated biomolecules whose electrostatics are described by the Poisson–Boltzmann (PB) equation. In a regularization method, by decomposing the potential function into two or three components, the singular component can be analytically represented by the Green’s function, while other components possess a higher regularity. Our new regularization combines the efficiency of two-component schemes with the accuracy of the three-component schemes. Based on this regularization, a new MIB finite difference algorithm is developed for solving both linear and nonlinear PB equations, where the nonlinearity is handled by using the inexact-Newton’s method. Compared with the existing MIB PB solver based on a three-component regularization, the present algorithm is simpler to implement by circumventing the work to solve a boundary value Poisson equation inside the molecular interface and to compute related interface jump conditions numerically. Moreover, the new MIB algorithm becomes computationally less expensive, while maintains the same second order accuracy. This is numerically verified by calculating the electrostatic potential and solvation energy on the Kirkwood sphere on which the analytical solutions are available and on a series of proteins with various sizes.
Poisson-Boltzmann equation; Elliptic interface problem; Electrostatics.
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@inproceedings{weihua2017a,
  title={A two-component Matched Interface and Boundary (MIB) regularization for charge singularity in implicit solvation},
  author={Weihua Geng, and Shan Zhao},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20200529105158166332693},
  booktitle={Journal of Computational Physics},
  volume={351},
  pages={25-39},
  year={2017},
}
Weihua Geng, and Shan Zhao. A two-component Matched Interface and Boundary (MIB) regularization for charge singularity in implicit solvation. 2017. Vol. 351. In Journal of Computational Physics. pp.25-39. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20200529105158166332693.
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