MIBPB: A software package for electrostatic analysis. The Poisson–Boltzmann equation (PBE) is an established model for the electrostatic analysis of biomolecules. The development of advanced computational techniques for the solution of the PBE has been an important topic in the past two decades. This article presents a matched interface and boundary (MIB)-based PBE software package, the MIBPB solver, for electrostatic analysis. The MIBPB has a unique feature that it is the first interface technique-based PBE solver that rigorously enforces the solution and flux continuity conditions at the dielectric interface between the biomolecule and the solvent. For protein molecular surfaces, which may possess troublesome geometrical singularities, the MIB scheme makes the MIBPB by far the only existing PBE solver that is able to deliver the second-order convergence, that is, the accuracy increases four times when the mesh size is halved. The MIBPB method is also equipped with a Dirichlet-to-Neumann mapping technique that builds a Green’s function approach to analytically resolve the singular charge distribution in biomolecules in order to obtain reliable solutions at meshes as coarse as 1 Å — whereas it usually takes other traditional PB solvers 0.25 Å to reach similar level of reliability. This work further accelerates the rate of convergence of linear equation systems resulting from the MIBPB by using the Krylov subspace (KS) techniques. Condition numbers of the MIBPB matrices are significantly reduced by using appropriate KS solver and preconditioner combinations. Both linear and nonlinear PBE solvers in the MIBPB package are tested by protein–solvent solvation energy calculations and analysis of salt effects on protein–protein binding energies, respectively. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2011

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  4. Han, Yihui; Chen, Huangxin; Wang, Xiao-Ping; Xie, Xiaoping: Extended HDG methods for second order elliptic interface problems (2020)
  5. Zhao, Rundong; Wang, Menglun; Chen, Jiahui; Tong, Yiying; Wei, Guo-Wei: The de Rham-Hodge analysis and modeling of biomolecules (2020)
  6. Hazra, Tania; Ullah, Sheik Ahmed; Wang, Siwen; Alexov, Emil; Zhao, Shan: A super-Gaussian Poisson-Boltzmann model for electrostatic free energy calculation: smooth dielectric distribution for protein cavities and in both water and vacuum states (2019)
  7. Li, Jiao; Ying, Jinyong; Lu, Benzhuo: A flux-jump preserved gradient recovery technique for accurately predicting the electrostatic field of an immersed biomolecule (2019)
  8. Quan, Chaoyu; Stamm, Benjamin; Maday, Yvon: A domain decomposition method for the Poisson-Boltzmann solvation models (2019)
  9. Zhang, Bo; Debuhr, Jackson; Niedzielski, Drake; Mayolo, Silvio; Lu, Benzhuo; Sterling, Thomas: DASHMM accelerated adaptive fast multipole Poisson-Boltzmann solver on distributed memory architecture (2019)
  10. Chen, Jiahui; Geng, Weihua: On preconditioning the treecode-accelerated boundary integral (TABI) Poisson-Boltzmann solver (2018)
  11. Dehghan, Mehdi; Abbaszadeh, Mostafa: Interpolating stabilized moving least squares (MLS) approximation for 2D elliptic interface problems (2018)
  12. Deng, Weishan; Xu, Jin; Zhao, Shan: On developing stable finite element methods for pseudo-time simulation of biomolecular electrostatics (2018)
  13. Egan, Raphael; Gibou, Frédéric: Fast and scalable algorithms for constructing solvent-excluded surfaces of large biomolecules (2018)
  14. Hu, Jingzhen; Zhao, Shan; Geng, Weihua: Accurate p(K_a) computation using matched interface and boundary (MIB) method based Poisson-Boltzmann solver (2018)
  15. Song, Lunji; Zhao, Shan; Liu, Kaifang: A relaxed weak Galerkin method for elliptic interface problems with low regularity (2018)
  16. Ying, Jinyong; Xie, Dexuan: A hybrid solver of size modified Poisson-Boltzmann equation by domain decomposition, finite element, and finite difference (2018)
  17. Zhong, Yimin; Ren, Kui; Tsai, Richard: An implicit boundary integral method for computing electric potential of macromolecules in solvent (2018)
  18. Cao, Yin; Wang, Bao; Xia, Kelin; Wei, Guowei: Finite volume formulation of the MIB method for elliptic interface problems (2017)
  19. Chen, Duan: Fractional Poisson-Nernst-Planck model for ion channels. I: Basic formulations and algorithms (2017)
  20. Chen, Long; Wei, Huayi; Wen, Min: An interface-fitted mesh generator and virtual element methods for elliptic interface problems (2017)

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