Journal publications

  1. C. Li, S. Zhao, B. Pentecost, Y. Ren, and Z. Guan, A fourth-order Cartesian grid method with FFT acceleration for elliptic and parabolic problems on irregular domains and arbitrarily curved boundaries, Journal of Scientific Computing, accepted, (2025).
  2. Y. Ren and S. Zhao, A multigrid-based fourth order finite difference method for elliptic interface problems with variable coefficients, International Journal of Numerical Analysis and Modeling, accepted, (2025).
  3. Y. Ren and S. Zhao, A high-order hybrid approach integrating neural networks and fast Poisson solvers for elliptic interface problems, Computation, 13, 83, (2025).
  4. S. Amihere, Y. Ren, W. Geng, and S. Zhao, A new boundary condition for the nonlinear Poisson-Boltzmann equation in electrostatic analysis of proteins, Journal of Computational Physics, 528, 113844, (2025).
  5. H. Yang, G. Long, Y. Ren, and S. Zhao, An augmented fourth order domain-decomposed method with fast algebraic solvers for three-dimensional Helmholtz interface problems, Journal of Computational Physics, 524, 113742, (2025).
  6. S.K. Pandey, A. Chakravorty, S. Zhao, and E. Alexov, On delivering polar solvation free energy of proteins from energy minimized structures using a regularized super-Gaussian Poisson-Boltzmann model, Journal of Computational Chemistry, 46, e27496, (2025).
  7. Y. Shao, Z. Chen, and S. Zhao, Modeling and analysis of ensemble average solvation energy and solute-solvent interfacial fluctuations, Computational and Mathematical Biophysics, 12, 20240017, (2024).
  8. Y. Shao, Z. Chen, and S. Zhao, A p-Laplacian approach and its analysis for the calculation of ensemble average solvation energy, Communications in Information and System, 24, 275-311, (2024).
  9. Y. Ren, S. Amihere, W. Geng, and S. Zhao, Comparison of three matched interface and boundary (MIB) schemes for solving the nonlinear Poisson-Boltzmann equation, Communications in Information and Systems, 24, 231-251, (2024).
  10. D. Nguyen, S. Mansur, L. Ciesla, N. Gray, S. Zhao, and Y. Bao, A combined computational and experimental approach to Study TrkB Binders for potential Neurodegenerative disease, Molecules, 29, 3992, (2024).
  11. H. Yang, S. Zhao, and G. Long, A MAC grid based FFT-AMIB solver for incompressible Stokes flows with interfaces and singular forces, Journal of Computational and Applied Mathematics, 450, 116019, (2024).
  12. 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, 45, 306-320, (2024).
  13. 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).
  14. 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).
  15. 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).
  16. 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).
  17. 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).
  18. 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).
  19. 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).
  20. 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).
  21. H. Feng and S. Zhao, A multigrid based finite difference method for solving parabolic interface problem, Electronic Research Archive, 29, 3141-3170, (2021).
  22. 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).
  23. 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).
  24. 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).
  25. ​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).
  26. H. Feng, G. Long, and S. Zhao, FFT-based high order central difference schemes for Poisson’s equation with staggered boundaries, Journal of Scientific Computing, 86, 7, (2021).​
  27. ​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).
  28. 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).​​
  29. 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).
  30. 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).
  31. 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).​
  32. 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).​
  33. 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).
  34. 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).
  35. 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).
  36. 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).
  37. 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).
  38. 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)
  39. 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).
  40. 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).
  41. 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).
  42. 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).
  43. 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).
  44. 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)
  45. ​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).
  46. 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).
  47. 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).
  48. 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).
  49. 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).
  50. 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).
  51. C. Li and S. Zhao, Efficient numerical schemes for fractional water wave models, Computers and Mathematics with Applications, 71, pp. 238-254, (2016).
  52. 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).
  53. 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).
  54. 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).
  55. 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).
  56. 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).
  57. 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).
  58. 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).
  59. 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).
  60. S. Zhao, Operator splitting ADI schemes for pseudo-time coupled nonlinear solvation simulations, Journal of Computational Physics, 257 , pp. 1000-1021, (2014).
  61. 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).
  62. 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).
  63. 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).
  64. 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).
  65. 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).
  66. 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).
  67. S. Zhao, High order FDTD methods for transverse electromagnetic systems in dispersive inhomogeneous media, Optics Letters, 36, pp. 3245-3247, (2011).
  68. 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).
  69. 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).
  70. 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).
  71. S. Zhao, High order vectorial analysis of waveguides with curved dielectric interfaces, IEEE Microwave and Wireless Components Letters , 19, pp. 266-268, (2009).
  72. 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).
  73. 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).
  74. 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).
  75. P. Bates, G.W. Wei and S. Zhao, Minimal molecular surfaces and their applications , Journal of Computational Chemistry, 29, pp. 380-391, (2008).
  76. 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).
  77. 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).
  78. Ge Wang, Haiou Shen, Wenxiang Cong, Shan Zhao and G.W. Wei, Temperature modulated bioluminescence tomography, Optics Express, 14(17), pp. 7852-7871, (2006).
  79. 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).
  80. S. Zhao and G.W. Wei, Option valuation by using discrete singular convolution, Applied Mathematics and Computation, 167, pp. 383-418, (2005).
  81. 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).
  82. 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).
  83. 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).
  84. 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).
  85. 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).
  86. 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).
  87. 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).
  88. 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).​
  89. 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).
  90. G.W. Wei and S. Zhao, Synchronization and information processing by an on-off coupling, Physical Review E,  65(5), 056210, (2002).

Peer-reviewed book chapter

  1. Y. Ren, C. Li, G. Long, and S. Zhao, A multigrid-based high order finite difference method for parabolic interface problems with variable coefficients, ICIAM2023 Special Issue on Recent Advances on two-phase flows, fluid-structure interactions, and interface problems, accepted, (2025).