Jump process for the trend estimation of time series. - Shan Zhao 001; Guo-Wei Wei 001 (Comput. Stat. Data Anal., 2003)

Comparison of the Discrete Singular Convolution and Three Other Numerical Schemes for Solving Fisher's Equation. - Shan Zhao 001; Guo-Wei Wei 001 (SIAM J. Sci. Comput., 2003)

Option valuation by using discrete singular convolution. - Shan Zhao 001; Guo-Wei Wei 001 (Appl. Math. Comput., 2005)

High order matched interface and boundary method for elliptic equations with discontinuous coefficients and singular sources. - Yongcheng Zhou; Shan Zhao 001; Michael Feig; Guo-Wei Wei 001 (J. Comput. Phys., 2006)

On the validity of "A proof that the discrete singular convolution (DSC)/Lagrange-distributed approximation function (LDAF) method is inferior to high order finite differences". - Guo-Wei Wei 001; Shan Zhao 001 (J. Comput. Phys., 2007)

Minimal molecular surfaces and their applications. - Peter W. Bates; Guo-Wei Wei 001; Shan Zhao 001 (J. Comput. Chem., 2008)

Mathematical Methods for Images and Surfaces. - Guowei Wei 001; Lalita Udpa; Yang Wang 020; Shan Zhao 001 (Int. J. Biomed. Imaging, 2010)

High order matched interface and boundary methods for the Helmholtz equation in media with arbitrarily curved interfaces. - Shan Zhao 001 (J. Comput. Phys., 2010)

Mathematical Methods for Images and Surfaces 2011. - Weihong Guo 002; Lalita Udpa; Yang Wang 020; Guowei Wei 001; Shan Zhao 001 (Int. J. Biomed. Imaging, 2012)

Weak Galerkin methods for second order elliptic interface problems. - Lin Mu; Junping Wang; Guowei Wei 001; Xiu Ye; Shan Zhao 001 (J. Comput. Phys., 2013)

High order FDTD methods for transverse magnetic modes with dispersive interfaces. - Duc Duy Nguyen; Shan Zhao 001 (Appl. Math. Comput., 2014)

Time-domain matched interface and boundary (MIB) modeling of Debye dispersive media with curved interfaces. - Duc Duy Nguyen; Shan Zhao 001 (J. Comput. Phys., 2014)

Operator splitting ADI schemes for pseudo-time coupled nonlinear solvation simulations. - Shan Zhao 001 (J. Comput. Phys., 2014)

A new discontinuous Galerkin method for the nonlinear Poisson-Boltzmann equation. - Weishan Deng; Xiaohe Zhufu; Jin Xu; Shan Zhao 001 (Appl. Math. Lett., 2015)

A new high order dispersive FDTD method for Drude material with complex interfaces. - Duc Duy Nguyen; Shan Zhao 001 (J. Comput. Appl. Math., 2015)

A Matched Alternating Direction Implicit (ADI) Method for Solving the Heat Equation with Interfaces. - Shan Zhao 001 (J. Sci. Comput., 2015)

Efficient numerical schemes for fractional water wave models. - Can Li; Shan Zhao 001 (Comput. Math. Appl., 2016)

A second order dispersive FDTD algorithm for transverse electric Maxwell's equations with complex interfaces. - Duc Duy Nguyen; Shan Zhao 001 (Comput. Math. Appl., 2016)

A new weak Galerkin finite element method for elliptic interface problems. - Lin Mu; Junping Wang; Xiu Ye; Shan Zhao 001 (J. Comput. Phys., 2016)

A matched Peaceman-Rachford ADI method for solving parabolic interface problems. - Chuan Li; Shan Zhao 001 (Appl. Math. Comput., 2017)

A two-component Matched Interface and Boundary (MIB) regularization for charge singularity in implicit solvation. - Weihua Geng; Shan Zhao 001 (J. Comput. Phys., 2017)

A Weak Galerkin Method with an Over-Relaxed Stabilization for Low Regularity Elliptic Problems. - Lunji Song; Kaifang Liu; Shan Zhao 001 (J. Sci. Comput., 2017)

A spatially second order alternating direction implicit (ADI) method for solving three dimensional parabolic interface problems. - Zhihan Wei; Chuan Li; Shan Zhao 001 (Comput. Math. Appl., 2018)

On developing stable finite element methods for pseudo-time simulation of biomolecular electrostatics. - Weishan Deng; Jin Xu; Shan Zhao 001 (J. Comput. Appl. Math., 2018)

Symmetric interior penalty Galerkin approaches for two-dimensional parabolic interface problems with low regularity solutions. - Lunji Song; Shan Zhao 001 (J. Comput. Appl. Math., 2018)

Reproducing ensemble averaged electrostatics with Super-Gaussian-based smooth dielectric function: application to electrostatic component of binding energy of protein complexes. - Shailesh Kumar Panday; Mihiri H. B. Shashikala; Arghya Chakravorty; Shan Zhao 001; Emil Alexov (Commun. Inf. Syst., 2019)

An augmented matched interface and boundary (MIB) method for solving elliptic interface problem. - Hongsong Feng; Guangqing Long; Shan Zhao 001 (J. Comput. Appl. Math., 2019)

Pseudo-transient ghost fluid methods for the Poisson-Boltzmann equation with a two-component regularization. - Sheik Ahmed Ullah; Shan Zhao 001 (Appl. Math. Comput., 2020)

A regularization approach for solving Poisson's equation with singular charge sources and diffuse interfaces. - Siwen Wang; Arum Lee; Emil Alexov; Shan Zhao 001 (Appl. Math. Lett., 2020)

Alternating direction ghost-fluid methods for solving the heat equation with interfaces. - Chuan Li; Zhihan Wei; Guangqing Long; Cameron Campbell; Stacy Ashlyn; Shan Zhao 001 (Comput. Math. Appl., 2020)

Capturing the Effects of Explicit Waters in Implicit Electrostatics Modeling: Qualitative Justification of Gaussian-Based Dielectric Models in DelPhi. - Arghya Chakravorty; Shailesh Kumar Panday; Swagata Pahari; Shan Zhao 001; Emil Alexov (J. Chem. Inf. Model., 2020)

FFT-based high order central difference schemes for three-dimensional Poisson's equation with various types of boundary conditions. - Hongsong Feng; Shan Zhao 001 (J. Comput. Phys., 2020)

A fourth order finite difference method for solving elliptic interface problems with the FFT acceleration. - Hongsong Feng; Shan Zhao 001 (J. Comput. Phys., 2020)

Adaptive pseudo-time methods for the Poisson-Boltzmann equation with Eulerian solvent excluded surface. - Benjamin Jones; Sheik Ahmed Ullah; Siwen Wang; Shan Zhao 001 (Commun. Inf. Syst., 2021)

Alternating Direction Implicit (ADI) Methods for Solving Two-Dimensional Parabolic Interface Problems with Variable Coefficients. - Chuan Li; Guangqing Long; Yiquan Li; Shan Zhao 001 (Comput., 2021)

Regularization methods for the Poisson-Boltzmann equation: Comparison and accuracy recovery. - Arum Lee; Weihua Geng; Shan Zhao 001 (J. Comput. Phys., 2021)

FFT-Based High Order Central Difference Schemes for Poisson's Equation with Staggered Boundaries. - Hongsong Feng; Guangqing Long; Shan Zhao 001 (J. Sci. Comput., 2021)

Benchmarking electrostatic free energy of the nonlinear Poisson-Boltzmann model for the Kirkwood sphere. - Sylvia Amihere; Weihua Geng; Shan Zhao 001 (Commun. Inf. Syst., 2022)

A FFT accelerated high order finite difference method for elliptic boundary value problems over irregular domains. - Yiming Ren; Hongsong Feng; Shan Zhao 001 (J. Comput. Phys., 2022)

A regularization approach for solving the super-Gaussian Poisson-Boltzmann model with heterogeneous dielectric functions. - Siwen Wang; Yuanzhen Shao; Emil Alexov; Shan Zhao 001 (J. Comput. Phys., 2022)

Convergence of a diffuse interface Poisson-Boltzmann (PB) model to the sharp interface PB model: A unified regularization formulation. - Yuanzhen Shao; Mark McGowan; Siwen Wang; Emil Alexov; Shan Zhao 001 (Appl. Math. Comput., 2023)

A FFT accelerated fourth order finite difference method for solving three-dimensional elliptic interface problems. - Yiming Ren; Shan Zhao 001 (J. Comput. Phys., 2023)

A Fast Sine Transform Accelerated High-Order Finite Difference Method for Parabolic Problems over Irregular Domains. - Chuan Li; Yiming Ren; Guangqing Long; Eric Boerman; Shan Zhao 001 (J. Sci. Comput., 2023)

A $p$-Laplacian approach and its analysis for the calculation of ensemble average solvation energy. - Zhan Chen; Shan Zhao 001; Yuanzhen Shao (Commun. Inf. Syst., 2024)

Comparison of three matched interface and boundary (MIB) schemes for solving the nonlinear Poisson-Boltzmann equation. - Yiming Ren; Sylvia Amihere; Weihua Geng; Shan Zhao 001 (Commun. Inf. Syst., 2024)

Bridging Eulerian and Lagrangian Poisson-Boltzmann solvers by ESES. - Sheik Ahmed Ullah; Xin Yang; Benjamin Jones; Shan Zhao 001; Weihua Geng; Guo-Wei Wei 001 (J. Comput. Chem., 2024)

Calculation of electrostatic free energy for the nonlinear Poisson-Boltzmann model based on the dimensionless potential. - Shan Zhao 001; Idowu E. Ijaodoro; Mark McGowan; Emil Alexov (J. Comput. Phys., 2024)

On delivering polar solvation free energy of proteins from energy minimized structures using a regularized super-Gaussian Poisson-Boltzmann model. - Shailesh Kumar Panday; Arghya Chakravorty; Shan Zhao 001; Emil Alexov (J. Comput. Chem., 2025)

A new boundary condition for the nonlinear Poisson-Boltzmann equation in electrostatic analysis of proteins. - Sylvia Amihere; Yiming Ren; Weihua Geng; Shan Zhao 001 (J. Comput. Phys., 2025)

An augmented fourth order domain-decomposed method with fast algebraic solvers for three-dimensional Helmholtz interface problems. - Huanfeng Yang; Guangqing Long; Yiming Ren; Shan Zhao 001 (J. Comput. Phys., 2025)

A Spatially Fourth-Order Cartesian Grid Method for Fast Solutions of Elliptic and Parabolic Problems on Irregular Domains with Sharply Curved Boundaries. - Chuan Li; Shan Zhao 001; Benjamin Pentecost; Yiming Ren; Zhen Guan (J. Sci. Comput., 2025)