Benner, Peter; Khoromskaia, Venera; Khoromskij, Boris; Kweyu, Cleophas; Stein, Matthias Regularization of Poisson-Boltzmann-type equations with singular source terms using the range-separated tensor format. (English) Zbl 1466.65180 SIAM J. Sci. Comput. 43, No. 1, A415-A445 (2021). MSC: 65N30 65N22 65F50 78A30 35Q20 35Q60 PDF BibTeX XML Cite \textit{P. Benner} et al., SIAM J. Sci. Comput. 43, No. 1, A415--A445 (2021; Zbl 1466.65180) Full Text: DOI OpenURL
Ji, Lijie; Chen, Yanlai; Xu, Zhenli A reduced basis method for the nonlinear Poisson-Boltzmann equation. (English) Zbl 07408418 Adv. Appl. Math. Mech. 11, No. 5, 1200-1218 (2019). MSC: 65N06 65N15 78A57 78M34 78M20 35Q20 35Q60 PDF BibTeX XML Cite \textit{L. Ji} et al., Adv. Appl. Math. Mech. 11, No. 5, 1200--1218 (2019; Zbl 07408418) Full Text: DOI arXiv OpenURL
Quan, Chaoyu; Stamm, Benjamin; Maday, Yvon A domain decomposition method for the polarizable continuum model based on the solvent excluded surface. (English) Zbl 1393.65054 Math. Models Methods Appl. Sci. 28, No. 7, 1233-1266 (2018). MSC: 65N35 65N55 35Q60 78A30 65F10 76T20 PDF BibTeX XML Cite \textit{C. Quan} et al., Math. Models Methods Appl. Sci. 28, No. 7, 1233--1266 (2018; Zbl 1393.65054) Full Text: DOI OpenURL
Zhong, Yimin; Ren, Kui; Tsai, Richard An implicit boundary integral method for computing electric potential of macromolecules in solvent. (English) Zbl 1383.78014 J. Comput. Phys. 359, 199-215 (2018). MSC: 78A30 78M15 78M16 35J05 92C40 PDF BibTeX XML Cite \textit{Y. Zhong} et al., J. Comput. Phys. 359, 199--215 (2018; Zbl 1383.78014) Full Text: DOI arXiv OpenURL
Geng, Weihua; Zhao, Shan A two-component matched interface and boundary (MIB) regularization for charge singularity in implicit solvation. (English) Zbl 1375.78008 J. Comput. Phys. 351, 25-39 (2017). MSC: 78A30 92C05 78M10 PDF BibTeX XML Cite \textit{W. Geng} and \textit{S. Zhao}, J. Comput. Phys. 351, 25--39 (2017; Zbl 1375.78008) Full Text: DOI OpenURL
Ying, Jinyong; Xie, Dexuan A new finite element and finite difference hybrid method for computing electrostatics of ionic solvated biomolecule. (English) Zbl 1349.78103 J. Comput. Phys. 298, 636-651 (2015). MSC: 78M20 78M10 65N06 65N30 78A48 PDF BibTeX XML Cite \textit{J. Ying} and \textit{D. Xie}, J. Comput. Phys. 298, 636--651 (2015; Zbl 1349.78103) Full Text: DOI OpenURL
Zhang, Bo; Peng, Bo; Huang, Jingfang; Pitsianis, Nikos P.; Sun, Xiaobai; Lu, Benzhuo Parallel AFMPB solver with automatic surface meshing for calculation of molecular solvation free energy. (English) Zbl 1344.78004 Comput. Phys. Commun. 190, 173-181 (2015). MSC: 78-04 78M16 78A70 65Y05 PDF BibTeX XML Cite \textit{B. Zhang} et al., Comput. Phys. Commun. 190, 173--181 (2015; Zbl 1344.78004) Full Text: DOI OpenURL
Li, Bo; Sun, Hui; Zhou, Shenggao Stability of a cylindrical solute-solvent interface: effect of geometry, electrostatics, and hydrodynamics. (English) Zbl 1328.35251 SIAM J. Appl. Math. 75, No. 3, 907-928 (2015). Reviewer: Jonathan Zinsl (München) MSC: 35Q92 76D07 78A30 35B35 76Z99 92C05 92C40 PDF BibTeX XML Cite \textit{B. Li} et al., SIAM J. Appl. Math. 75, No. 3, 907--928 (2015; Zbl 1328.35251) Full Text: DOI Link OpenURL
Xie, Dexuan; Li, Jiao A new analysis of electrostatic free energy minimization and Poisson-Boltzmann equation for protein in ionic solvent. (English) Zbl 1298.78036 Nonlinear Anal., Real World Appl. 21, 185-196 (2015). MSC: 78M30 35Q60 78A30 PDF BibTeX XML Cite \textit{D. Xie} and \textit{J. Li}, Nonlinear Anal., Real World Appl. 21, 185--196 (2015; Zbl 1298.78036) Full Text: DOI OpenURL
Cooper, Christopher D.; Bardhan, Jaydeep P.; Barba, L. A. A biomolecular electrostatics solver using python, GPUs and boundary elements that can handle solvent-filled cavities and stern layers. (English) Zbl 1360.78047 Comput. Phys. Commun. 185, No. 3, 720-729 (2014). MSC: 78M15 78A70 78A30 PDF BibTeX XML Cite \textit{C. D. Cooper} et al., Comput. Phys. Commun. 185, No. 3, 720--729 (2014; Zbl 1360.78047) Full Text: DOI arXiv Link OpenURL
Xie, Dexuan New solution decomposition and minimization schemes for Poisson-Boltzmann equation in calculation of biomolecular electrostatics. (English) Zbl 1349.78077 J. Comput. Phys. 275, 294-309 (2014). MSC: 78M10 78A30 65N30 92C40 PDF BibTeX XML Cite \textit{D. Xie}, J. Comput. Phys. 275, 294--309 (2014; Zbl 1349.78077) Full Text: DOI OpenURL
Geng, Weihua; Krasny, Robert A treecode-accelerated boundary integral Poisson-Boltzmann solver for electrostatics of solvated biomolecules. (English) Zbl 1349.78084 J. Comput. Phys. 247, 62-78 (2013). MSC: 78M15 65N38 78A30 92C30 PDF BibTeX XML Cite \textit{W. Geng} and \textit{R. Krasny}, J. Comput. Phys. 247, 62--78 (2013; Zbl 1349.78084) Full Text: DOI OpenURL
Geng, Weihua; Jacob, Ferosh A GPU-accelerated direct-sum boundary integral Poisson-Boltzmann solver. (English) Zbl 1310.78017 Comput. Phys. Commun. 184, No. 6, 1490-1496 (2013). MSC: 78M15 78A30 78-04 PDF BibTeX XML Cite \textit{W. Geng} and \textit{F. Jacob}, Comput. Phys. Commun. 184, No. 6, 1490--1496 (2013; Zbl 1310.78017) Full Text: DOI arXiv OpenURL
Harris, Robert C.; Mackoy, Travis; Fenley, Marcia O. A stochastic solver of the generalized Born model. (English) Zbl 1278.82072 Mol. Based Math. Biol. 1, 63-74 (2013). MSC: 82D60 92D20 78A30 35Q20 PDF BibTeX XML Cite \textit{R. C. Harris} et al., Mol. Based Math. Biol. 1, 63--74 (2013; Zbl 1278.82072) Full Text: DOI OpenURL
Aksoylu, Burak; Bond, Stephen D.; Cyr, Eric C.; Holst, Michael Goal-oriented adaptivity and multilevel preconditioning for the Poisson-Boltzmann equation. (English) Zbl 1263.78011 J. Sci. Comput. 52, No. 1, 202-225 (2012). Reviewer: Jong Hyuk Park (Ulsan) MSC: 78M10 35Q20 65N30 65N55 65F08 78A35 78A30 65N15 PDF BibTeX XML Cite \textit{B. Aksoylu} et al., J. Sci. Comput. 52, No. 1, 202--225 (2012; Zbl 1263.78011) Full Text: DOI arXiv OpenURL
Xie, Dexuan; Scott, L. Ridgway A new boundary integral equation for molecular electrostatics with charges over whole space. (English) Zbl 1255.78011 BIT 51, No. 4, 1051-1071 (2011). Reviewer: Pierluigi Maponi (Camerino) MSC: 78A30 65R20 92B05 PDF BibTeX XML Cite \textit{D. Xie} and \textit{L. R. Scott}, BIT 51, No. 4, 1051--1071 (2011; Zbl 1255.78011) Full Text: DOI OpenURL
Xu, Zhenli; Cai, Wei Fast analytical methods for macroscopic electrostatic models in biomolecular simulations. (English) Zbl 1228.92008 SIAM Rev. 53, No. 4, 683-720 (2011). MSC: 92C05 65Y20 78A70 35J15 78A35 92C40 35Q92 PDF BibTeX XML Cite \textit{Z. Xu} and \textit{W. Cai}, SIAM Rev. 53, No. 4, 683--720 (2011; Zbl 1228.92008) Full Text: DOI Link OpenURL
Chaudhry, Jehanzeb Hameed; Bond, Stephen D.; Olson, Luke N. Finite element approximation to a finite-size modified Poisson-Boltzmann equation. (English) Zbl 1230.78026 J. Sci. Comput. 47, No. 3, 347-364 (2011). MSC: 78M10 78A30 PDF BibTeX XML Cite \textit{J. H. Chaudhry} et al., J. Sci. Comput. 47, No. 3, 347--364 (2011; Zbl 1230.78026) Full Text: DOI Link OpenURL
Geng, Weihua; Wei, G. W. Multiscale molecular dynamics using the matched interface and boundary method. (English) Zbl 1246.82028 J. Comput. Phys. 230, No. 2, 435-457 (2011). MSC: 82B24 78A70 82-08 92C40 PDF BibTeX XML Cite \textit{W. Geng} and \textit{G. W. Wei}, J. Comput. Phys. 230, No. 2, 435--457 (2011; Zbl 1246.82028) Full Text: DOI Link OpenURL
Lu, Benzhuo; Cheng, Xiaolin; Huang, Jingfang; McCammon, J. Andrew AFMPB: an adaptive fast multipole Poisson-Boltzmann solver for calculating electrostatics in biomolecular systems. (English) Zbl 1220.78002 Comput. Phys. Commun. 181, No. 6, 1150-1160 (2010). Reviewer: Teodora-Liliana Rădulescu (Craiova) MSC: 78-04 78M16 78A70 PDF BibTeX XML Cite \textit{B. Lu} et al., Comput. Phys. Commun. 181, No. 6, 1150--1160 (2010; Zbl 1220.78002) Full Text: DOI OpenURL
Grandison, Scott; Penfold, Robert; Vanden-Broeck, Jean-Marc A rapid boundary integral equation technique for protein electrostatics. (English) Zbl 1123.78010 J. Comput. Phys. 224, No. 2, 663-680 (2007). Reviewer: Stanislaw Janeczko (Warszawa) MSC: 78A70 78M15 92C40 65N38 PDF BibTeX XML Cite \textit{S. Grandison} et al., J. Comput. Phys. 224, No. 2, 663--680 (2007; Zbl 1123.78010) Full Text: DOI OpenURL
Xin, Weidong; Juffer, André H. A boundary element formulation of protein electrostatics with explicit ions. (English) Zbl 1115.92007 J. Comput. Phys. 223, No. 1, 416-435 (2007). Reviewer: Gunther Schmidt (Berlin) MSC: 92C05 92C40 78A70 65N38 PDF BibTeX XML Cite \textit{W. Xin} and \textit{A. H. Juffer}, J. Comput. Phys. 223, No. 1, 416--435 (2007; Zbl 1115.92007) Full Text: DOI OpenURL
Qiao, Zhonghua; Li, Zhilin; Tang, Tao A finite difference scheme for solving the nonlinear Poisson-Boltzmann equation modeling charged spheres. (English) Zbl 1105.78015 J. Comput. Math. 24, No. 3, 252-264 (2006). Reviewer: Vladislav V. Kravchenko (Queretaro) MSC: 78M20 65N06 78A35 PDF BibTeX XML Cite \textit{Z. Qiao} et al., J. Comput. Math. 24, No. 3, 252--264 (2006; Zbl 1105.78015) OpenURL
Tsukerman, Igor A class of difference schemes with flexible local approximation. (English) Zbl 1082.65108 J. Comput. Phys. 211, No. 2, 659-699 (2006). Reviewer: Ariadna Lucia Pletea (Iaşi) MSC: 65N06 35J05 78M20 78A40 78A45 82C80 PDF BibTeX XML Cite \textit{I. Tsukerman}, J. Comput. Phys. 211, No. 2, 659--699 (2006; Zbl 1082.65108) Full Text: DOI OpenURL
Rocchia, W. Poisson-Boltzmann equation boundary conditions for biological applications. (English) Zbl 1080.92009 Math. Comput. Modelling 41, No. 10, 1109-1118 (2005). MSC: 92C05 65N06 78A70 PDF BibTeX XML Cite \textit{W. Rocchia}, Math. Comput. Modelling 41, No. 10, 1109--1118 (2005; Zbl 1080.92009) Full Text: DOI OpenURL
Tuszyński, J. A.; Brown, J. A.; Crawford, E.; Carpenter, E. J.; Nip, M. L. A.; Dixon, J. M.; Satarić, M. V. Molecular dynamics simulations of tubulin structure and calculations of electrostatic properties of microtubules. (English) Zbl 1081.92020 Math. Comput. Modelling 41, No. 10, 1055-1070 (2005). MSC: 92C40 92C05 92C37 78A70 PDF BibTeX XML Cite \textit{J. A. Tuszyński} et al., Math. Comput. Modelling 41, No. 10, 1055--1070 (2005; Zbl 1081.92020) Full Text: DOI OpenURL