## Journal publications

- S. Ahmed Ullah, X. Yang, B. Jones, S. Zhao, W. Geng, and G.W. Wei, Bridging Eulerian and Lagrangian Poisson-Boltzmann solvers by ESES, Journal of Computational Chemistry, accepted, (2023).
- S. Zhao, I. Ijaodoro, M. McGowan, E. Alexov, Calculation of electrostatic free energy for the nonlinear Poisson-Boltzmann model based on the dimensionless potential,
*Journal of Computational Physics*, 497, 112634, (2024). - C. Li, Y. Ren, G. Long, E. Boerman, and S. Zhao, A fast Sine transform accelerated high order finite difference method for parabolic problems over irregular domains,
*Journal of Scientific Computing*,**95,**49 (2023). - Y. Ren and S. Zhao, A FFT accelerated fourth order finite difference method for solving three-dimensional elliptic interface problems,
*Journal of Computational Physics*,**477**, 111924, (2023). - Y. Shao, M. McGowan, S. Wang, E. Alexov, and S. Zhao, Convergence of a diffuse interface Poisson-Boltzmann (PB) model to the sharp interface PB model: a unified regularization formulation,
*Applied Mathematics and Computation*,**436**, 127501, (2023). - S. Amihere, W. Geng, and S. Zhao, Benchmarking electrostatic free energy of the nonlinear Poisson-Boltzmann model for the Kirkwood sphere,
*Communications in Information & Systems*,**22(3)**, 305-315, (2022). - S. Wang, Y. Shao, E. Alexov, and S. Zhao, A regularization approach for solving the super-Gaussian Poisson-Boltzmann model with heterogeneous dielectric functions,
*Journal of Computational Physics*,**464**, 111340, (2022). - T. Hazra and S. Zhao, Physics-guided multiple regression analysis for calculating electrostatic free energies of proteins in different reference states,
*Communications in Information & Systems*,**22(2)**, 187-221, (2022). - Y. Ren, H. Feng, and S. Zhao, A FFT accelerated high order finite difference method for elliptic boundary value problems over irregular domains,
*Journal of Computational Physics,***448,**110762, (2022). - H. Feng and S. Zhao, A multigrid based finite difference method for solving parabolic interface problem,
*Electronic Research Archive*,**29**, 3141-3170, (2021). - C. Li, G. Long, Y. Li, and S. Zhao, Alternating Direction Implicit (ADI) methods for solving two dimensional parabolic interface problems with variable coefficients,
*Computation*,**9(7)**, 79, (2021). - K. Liu, L. Song, and S. Zhao, A new over-penalized weak Galerkin method. Part I: Second order elliptic problems,
*Discrete and Continuous Dynamical Systems Series B*,**26**, 2411-2428, (2021). - B. Jones, S. Ahmed Ullah, S. Wang, and S. Zhao, Adaptive pseudo-time methods for the Poisson-Boltzmann equation with Eulerian solvent excluded surface,
*Communications in Information & Systems*,**21**(1), 85-123, (2021). - S. Wang, E. Alexov, and S. Zhao, On regularization of charge singularities in solving the Poisson-Boltzmann equation with a smooth solute-solvent boundary,
*Mathematical Biosciences and Engineering*,**18**(2) 1370-1405, (2021). - H. Feng, G. Long, and S. Zhao, FFT-based high order central difference schemes for Poisson's equation with staggered boundaries, J
*ournal of Scientific Computing*,**86**, 7, (2021). - A. Lee, W. Geng, and S. Zhao, Regularization methods for the Poisson-Boltzmann equation: comparison and accuracy recovery,
*Journal of Computational Physics*,**426**, 109958, (2021). - C. Li, M. McGowan, E. Alexov, and S. Zhao, A Newton-like iterative method implemented in the DelPhi for solving the nonlinear Poisson-Boltzmann equation,
*Mathematical Biosciences and Engineering*,**17(6)**, 6259-6277, (2020). - H. Feng and S. Zhao, A fourth order finite difference method for solving elliptic interface problems with the FFT acceleration,
*Journal of Computational Physics*,**419**, 109677, (2020). - S. Ahmed Ullah and S. Zhao, Pseudo-transient ghost fluid methods for the Poisson-Boltzmann equation with a two-component regularization,
*Applied Mathematics and Computation*,**380**, 125267, (2020). - C. Li, Z. Wei, G. Long, C. Campbell, S. Ashlyn, and S. Zhao, Alternating direction ghost-fluid methods for solving the heat equation with interfaces,
*Computers and Mathematics with Applications*,**80**, 714-732, (2020). - H. Feng and S. Zhao, FFT-based high order central difference schemes for the three-dimensional Poisson equation with various types of boundary conditions,
*Journal of Computational Physics*,**410**, 109391, (2020). - A. Chakravorty, S. Pandey, S. Pahari, S. Zhao, and E. Alexov, Capturing the effects of explicit waters in implicit electrostatics modeling: Qualitative justification of Gaussian-based dielectric models in DelPhi,
*Journal of Chemical Information and Modeling*,**60**, 2229-2246, (2020). - S. Wang, A. Lee, E. Alexov, and S. Zhao, A regularization approach for solving Poisson's equation with singular charge sources and diffuse interfaces,
*Applied Mathematics Letters*,**102**, 106144, (2020). - SK Panday, MHB Shashikala, A. Chakravorty, S. Zhao and E. Alexov, Reproducing ensemble averaged electrostatics with Super-Gaussian-based smooth dielectric function: Application to electrostatic component of binding energy of protein complexes,
*Communications in Information and Systems*,**19**, 405-423, (2019). - H. Feng, G. Long, and S. Zhao, An augmented matched interface and boundary (MIB) method for solving elliptic interface problem,
*Journal of Computational and Applied Mathematics*,**361**, 426-433, (2019). - T. Hazra, S. Ahmed-Ullah, S. Wang, E. Alexov, and S. Zhao, A super-Gaussian Poisson-Boltzmann model for electrostatic solvation free energy calculation: smooth dielectric distribution for protein cavities and in both water and vacuum states,
*Journal of Mathematical Biology*,**79**, 631-672, (2019). - C. Arghya, Z. Jia, L. Li, S. Zhao, and E. Alexov, Reproducing the ensemble average polar solvation energy of a protein from a single structure: Gaussian-based smooth dielectric function for macromolecular modeling,
*Journal of Chemical Theory and Computation*,**14**, 1020-1032, (2018) - Z. Wei, C. Li, and S. Zhao, A spatially second order alternating direction implicit (ADI) method for three dimensional parabolic interface problems,
*Computers and Mathematics with Applications*,**75**, 2173-2192, (2018). - L. Song, S. Zhao, and K. Liu, A relaxed weak Galerkin method for elliptic interface problems with low regularity, Applied Numerical Mathematics,
**128**, 65-80, (2018). - J. Hu, S. Zhao, and W. Geng, Accurate pKa computation using matched interface and boundary (MIB) method based Poisson-Boltzmann solver,
*Communication in Computational Physics*,**23**, 520-539, (2018). - W. Deng, J. Xu, and S. Zhao, On developing stable finite element methods for pseudo-time simulation of biomolecular electrostatics,
*Journal of Computational and Applied Mathematics*,**330**, 456-474, (2018). - L. Song and S. Zhao, Symmetric interior penalty Galerkin approaches for tow-dimensional parabolic interface problems with low regularity solutions,
*Journal of Computational and Applied Mathematics*,**330**, 356-379, (2018). - W. Geng and S. Zhao, A two-component Matched Interface and Boundary (MIB) regularization for charge singularity in implicit solvation,
*Journal of Computational Physics*,**351**, 25-39, (2017) - L. Song, K. Liu, and S. Zhao, A weak Galerkin method with an over-relaxed stabilization for low regularity elliptic problems,
*Journal of Scientific Computing*,**71**, 195-218, (2017). - C. Li and S. Zhao, A matched Peaceman-Rachford ADI method for solving parabolic interface problems,
*Applied Mathematics and Computation*,**299**, pp. 28-44, (2017). - L. Wilson and S. Zhao, Unconditionally stable time splitting methods for the electrostatic analysis of solvated biomolecules,
*International Journal of Numerical Analysis and Modeling*,**13**, pp. 852-878, (2016). - L. Mu, J. Wang, X. Ye, and S. Zhao, A new weak Galerkin finite element method for elliptic interface problems,
*Journal of Computational Physics,***325,**pp. 157-173, (2016). - D.D. Nguyen and S. Zhao, A second order dispersive FDTD algorithm for transverse electric Maxwell's equations with complex interfaces,
*Computers and Mathematics with Applications,***71,**pp. 1010-1035, (2016). - Y. Zhang, D.D. Nguyen, K. Du, J. Xu, and S. Zhao, Time-domain numerical solutions of Maxwell interface problems with discontinuous electromagnetic waves,
*Advances in Applied Mathematics and Mechanics*,**8,**pp. 353-385, (2016). - C. Li and S. Zhao, Efficient numerical schemes for fractional water wave models,
*Computers and Mathematics with Applications,***71,**pp. 238-254, (2016). - W. Deng, X. Zhufu, J. Xu, and S. Zhao, A new discontinuous Galerkin method for the nonlinear Poisson-Boltzmann equation,
*Applied Mathematics Letters*,**49,**pp. 126-132, (2015). - D.D. Nguyen and S. Zhao, A new high order dispersive FDTD method for Drude material with complex interfaces,
*Journal of Computational and Applied Mathematics,***285**, pp. 1-14, (2015). - Y.-B. Yuan, Y.D. Gao, and S. Zhao, Editorial: Machine learning in intelligent video and automated monitoring,
*The Scientific World Journal,***2015**570145, (2015). - S. Zhao, A matched alternating direction implicit (ADI) method for solving the heat equation with interfaces,
*Journal of Scientific Computing,***63**, pp. 118-137, (2015). - Duc D. Nguyen and S. Zhao, Time-domain matched interface and boundary (MIB) modeling of Debye dispersive media with curved interfaces,
*Journal of Computational Physics,***278**, pp. 298-325, (2014). - L. Mu, J. Wang, X. Ye, and S. Zhao, A numerical study on the weak Galerkin method for the Helmholtz equation,
*Communication in Computational Physics,***15**, pp. 1461-1479, (2014). - S. Zhao and G.W. Wei, A unified discontinuous Galerkin framework for time integration,
*Mathematical Methods in the Applied Sciences,***37**, pp. 1042-1071, (2014). - Wufeng Tian and S. Zhao, A fast ADI algorithm for geometric flow equations in biomolecular surface generation,
*International Journal for Numerical Methods in Biomedical Engineering,***30**, pp. 490-516, (2014). - Duc D. Nguyen and S. Zhao, High order FDTD methods for transverse magnetic modes with dispersive interfaces,
*Applied Mathematics and Computation,***226**, pp. 699-707, (2014). - S. Zhao, Operator splitting ADI schemes for pseudo-time coupled nonlinear solvation simulations,
*Journal of Computational Physics,***257**, pp. 1000-1021, (2014). - L. Mu, J. Wang, X. Ye, G.W. Wei, and S. Zhao, Weak Galerkin methods for second order elliptic interface problems,
*Journal of Computational Physics,***250**, pp. 106-125, (2013). - S. Rosencrans, X. Wang, and S. Zhao, Estimating eigenvalues of an anisotropic thermal tensor from transient thermal probe measurements,
*Discrete and Continuous Dynamics Systems,***33**, pp. 5441-5455,(2013). - W. Geng and S. Zhao, Fully implicit ADI schemes for solving the nonlinear Poisson-Boltzmann equation,
*Molecular Based Mathematical Biology,***1**, pp. 109 - 123, (2013). - Zhan Chen, S. Zhao, Jaehun Chun, Dennis G. Thomas, Nathan A. Baker, Peter W. Bates, and G.W. Wei, Variational approach for nonpolar solvation analysis,
*Journal of Chemical Physics,***137**, 084101, (2012). - Weihong Guo, Lalita Udpa, Yang Wang, G.W. Wei, and S. Zhao, Editorial: Mathematical Methods for Images and Surfaces 2011,
*International Journal of Biomedical Imaging,***2012**, 419647, (2012). - S. Zhao, Pseudo-time coupled nonlinear models for biomolecular surface representation and solvation analysis,
*International Journal for Numerical Methods in Biomedical Engineering,***27**, pp. 1964-1981, (2011). - Pengfei Yao and S. Zhao, A new boundary closure scheme for the multiresolution time-domain (MRTD) method,
*IEEE Transaction on Antennas and Propagation,***59**, pp. 3305-3312, (2011). - S. Zhao, High order FDTD methods for transverse electromagnetic systems in dispersive inhomogeneous media,
*Optics Letters,***36**, pp. 3245-3247, (2011). - G.W. Wei, Lalita Udpa, Yang Wang, and S. Zhao, Editorial: Mathematical Methods for Images and Surfaces,
*International Journal of Biomedical Imaging,***2010**, 918467, (2010). - S. Zhao, A fourth order finite difference method for waveguides with curved perfectly conducting boundaries,
*Computer Methods in Applied Mechanics and Engineering,***199**, pp. 2655-2662, (2010). - S. Zhao, High order matched interface and boundary methods for the Helmholtz equation in media with arbitrarily curved interfaces,
*Journal of Computational Physics*,**229**, pp. 3155-3170, (2010). - P. Bates, Z. Chen, Y. Sun, G.W. Wei, and S. Zhao, Geometric and potential driving formation and evolution of biomolecular surfaces,
*Journal of Mathematical Biology*,**59**, pp. 193-231, (2009). - S. Zhao, High order vectorial analysis of waveguides with curved dielectric interfaces,
*IEEE Microwave and Wireless Components Letters*,**19**, pp. 266-268, (2009). - S. Rosencrans, X. Wang, W. Winter, and S. Zhao, Measuring the insulating ability of anisotropic thermal conductors via principal Dirichlet eigenvalue,
*European Journal of Applied Mathematics*,**20**, pp. 231-246, (2009). - S. Zhao and G.W. Wei, Matched interface and boundary (MIB) for the implementation of boundary conditions in high order central finite differences,
*International Journal for Numerical Methods in Engineering,*,**77**, pp. 1690-1730, (2009). - S. Zhao, Full-vectorial matched interface and boundary (MIB) method for the modal analysis of dielectric waveguides,
*IEEE/OSA Journal of Lightwave Technology*,**26**, pp. 2251-2259, (2008). - P. Bates, G.W. Wei and S. Zhao, Minimal molecular surfaces and their applications ,
*Journal of Computational Chemistry*,**29**, pp. 380-391, (2008). - S. Zhao, On the spurious solutions in the high-order finite difference methods for eigenvalue problems,
*Computer Methods in Applied Mechanics and Engineering*,**196**, pp. 5031-5046, (2007). - G.W. Wei and S. Zhao, On the validity of "A proof that the discrete singular convolution (DSC)/Langrange-distributed approximation function (LDAF) method is inferior to high order finite differences",
*Journal of Computational Physics*,**226**, pp. 2389-2392, (2007). - Ge Wang, Haiou Shen, Wenxiang Cong, Shan Zhao and G.W. Wei, Temperature modulated bioluminescence tomography,
*Optics Express*,**14(17)**, pp. 7852-7871, (2006). - Y.C. Zhou, S. Zhao, M. Feig, and G.W. Wei, High order matched interface and boundary method for elliptic equations with discontinuous coefficients and singular sources,
*Journal of Computational Physics*,**213**, pp. 1-30, (2006). - S. Zhao and G.W. Wei, Option valuation by using discrete singular convolution,
*Applied Mathematics and Computation*,**167**, pp. 383-418, (2005). - S.N. Yu, S. Zhao, and G.W. Wei, Local spectral time-splitting method for first and second order partial differential equations,
*Journal of Computational Physics*,**206**, pp. 727-780, (2005). - S. Zhao, G.W. Wei, and Y. Xiang, DSC analysis of free-edged beams by an iteratively matched boundary method,
*Journal of Sound and Vibration*,**284**, pp. 487-493, (2005). - S. Zhao and G.W. Wei, High-order FDTD methods via derivative matching for Maxwell's equations with material interfaces,
*Journal of Computational Physics*,**200**, pp. 60-103, (2004). - S. Zhao and G.W. Wei, Tensor product derivative matching for wave propagation in inhomogeneous media,
*Microwave and Optical Technology Letters*,**43-1**, pp. 69-77, (2004). - G. Bao, G.W. Wei, and S. Zhao, Numerical solution of the Helmholtz equation with high wavenumbers,
*International Journal for Numerical Methods in Engineering*,**59**, pp. 389-408, (2004). - S. Zhao and G.W. Wei, Comparison of the discrete singular convolution and three other numerical schemes for solving Fisher's equation,
*SIAM Journal on Scientific Computing*,**25**, pp. 127-147, (2003). - Z.H. Shao, G.W. Wei, and S. Zhao, DSC time-domain solution of Maxwell's equations,
*Journal of Computational Physics*,**189**, pp. 427-453, (2003). - G. Bao, G.W. Wei, and S. Zhao, Local spectral time-domain method for electromagnetic wave propagation,
*Optics Letters*,**28(7)**, pp. 513-515, (2003). - S. Zhao and G.W. Wei, Jump process for the trend estimation of time series,
*Computational Statistics and Data Analysis,***42(1-2)**, pp. 219-241, (2003). - G.W. Wei and S. Zhao, Synchronization and information processing by an on-off coupling,
*Physical Review E*,**65(5)**, 056210, (2002).