RESEARCH AND PREPRINTS
My research field is numerical solutions for partial differential equations. As matter of fact my major as a undergraduate student was Computational Mathematics, though the first two years we took the same courses with the pure math majors. My focus for graduate study in China was numerical solutions for partial differential equations.
My current research interest focuses on numerical solutions for stochastic partial differential equations and integral equations, with applications to interface problems for flows in porous media, optimal controls for random interface problems, and optimal controls of mathematical biology problems such as vector born diseases.
1. Modeling and numerical simulations for flows in karest aquifers.
2. Numerical solutions for stochastic partial differential equations and nonlinear filter problems.
3. Numerical methods for flow in poroelastic media
4. Backward doubly stochastic differential equation methods for nonlinear filtering problems
Max Gunzburger, FSU, stochastic partial differential equations, flow in porous media
A. J. Meir, Auburn University, Flow in poroelastic media
Song Chen, University of Wisconsin at La Crosse, Flow in poroelastic media, bioconvenction models
Feng Bao, Auburn, Numerical methods for nonlinear filter problems
Xiaoying Han, Auburn University, Numerical methods for nonlinear filter problems
Yuehseng Xu, Syracuse University, stochastic integral equations
Ying Jiang, Sun Yat-sen University, Stochastic PDES.
Junshan Lin, Auburn,
Hongmei Chi, FAMU, Efficient quasi-Monte Carlo method
Werner Van Wyk, Auburn, Stochastic optimization.
Bao, Zhejiang University. Stochastic interface problems.
Kai Zhang, Stochastic interface problems.
and Yanzhao Cao, A posterior estimations of cell
functional finite volume methods, accepted by Journal of
Computational and Applied Mathematics.
Feng Bao, Yanzhao Cao, and Hongmei Chi, On BSDE method for nonlinear filtering problems with jump processes, accepted by International Journal of Uncertainty Quantification.
Linjun Wang, Yanzhao Cao, A hybrid collocation method for fractional initial value problems, accepted by Journal of Integral Equations and Applications.
Gang Bao, Yanzhao
Cao, Junshan Lin, and Hans Werner Van Wyk, Optimal
design of random rough surfaces in thin-film solar cells,
Communications in Computational Physics,
Jingyuan Zhang, Yanzhao Cao, and Hongxing Rui, A partitioned method with different time steps for coupled Stokes and Carcy flows with transport, International Journal of Numerical Analysis and Modeling, 163(2), 463-498 (2019).
Gang Bao, Yanzhao Cao, Yongke Hao, and Kai Zhang, A robust numerical method for the random interface grating problem via shape calculus, weak Galerkin method, and low-rank approximation, Journal of Scientific Computing,
Jialin Hong, and Zhihui Liu, Finite element approximations for
second-order stochastic differential equation driven by
fractional Brownian motion, IMA Journal of
Numerical Analysis, 38, 184--197 (2018).
Feng Bao, Yanzhao Cao, and Weidong Zhao, A backward doubly stochastic differential equation approach for nonlinear filtering problems, Communications in Computational Physics, 23, 1573--1601 (2018).
Shimin Chai, Yanzhao Cao, Yongkui Zou, and Wenju Zhao, Conforming finite element methods for the stochastic Cahn--Hilliard--Cook equation, Applied Numerical Mathematics, 124, 44--56 (2018).
Yanzhao Cao, Jialin Hong, and Zhihui Liu, Approximating stochastic evolution equations with additive white and rough noises, SIAM Journal on Numerical Analysis, 55(4), 1958--1981 (2017).
Yanzhao Cao, Clayton Webster, and Guannan Zhang,
An efficient meshfree implicit filter for nonlinear filtering
problems, I. J. UQ, 6(1), 19-33 (2016).
Feng Bao, Yanzhao Cao,
A. J. Meir, and Weidong Zhao, A first order
scheme for backward doubly stochastic differential
equations, SIAM Journal on
4(1), 413-445 (2016).
Yanzhao Cao and Dawit Denu, Analysis of stochastic vector-host epidemic model with direct transmission, DCDS-B, 21(7), 2109-2127 (2016).
F. Bao, Yanzhao Cao, W. Zhao and B. Hu, Identification of hydraulic conductivity distributions in density dependent flow fields of submarine groundwater discharge modeling using adjoint-state, SCIENCE CHINA Earth Sciences, doi:10.1007/s11430-015-5236-x (2016).
Yanzhao Cao, Song Chen, and Leo Rebholz, Well-posedness and a numerical study of a regularization model with adaptive nonlinear filtering for incompressible fluid flow, Computers & Mathematics with Applications, 71(11), 2192-2205 (2016).
Cao, Song Chen, and A. J. Meir, Quasi-linear
poroelasticity: analysis and hybrid finite element
approximations, Numer. Meth. PDEs, Vol.
31, no 4, 1174--1189 (2015).
Feng Bao, Yanzhao Cao, and Weidong Zhao, High order numerical algorithms for forward backward doubly stochastic differential equations, accepted by Discrete and Continuous Dynamical System-B, Vol. 20, no 5, 1297--1313 (2015).
Adanur, Yang Shen, A. J. Meir, and Yanzhao Cao, Finite
Element Analysis of Monofilament Woven Fabrics under Uniaxial
Tension, The Journal of the Textile
Institute, Vol. 106, no 1, 90--100 (2015)
Yanzhao Cao and Zhang, Ran, A stochastic collocation method for stochastic Volterra equations of the second kind. J. Integral Equations Appl. Vol. 27, no. 1, 1--25 (2015).
Yanzhao Cao, O.
A. IIhan, and S. A. Alimov, On the problems of
peridynamics with special convolution kernels, Journal
of Integral Equations and Applications,
Vol. 26, No. 3, 301-321 (2014).
Yanzhao Cao, Ying Jiang and Yuesheng Xu, A Fast algorithm for orthogonal polynomial expansions on sparse grids, Journal of Complexity , Vol. 30, No. 6, 673-682 (2014)
Yanzhao Cao, Gunzburger, Max; He, Xiaoming; Wang, Xiaoming, Parallel non-iterative multi-physics domain decomposition methods for the time-dependent Stokes-Darcy model, Mathematics of Computation, Vol. 83 no. 288, 1617--1644 (2014).
Feng Wang and Xiaoshen Wang, Homotopy continuation
methods for stochastic two-point boundary value problems
driven by additive noises, Journal of
Computational Mathematics, Vol.32,
No.6, 630--642 (2014).
Yanzhao Cao, Feng Bao and Xiaoying Han, An accurate and stable numerical algorithm for nonlinear filtering problems, Commun. Comput. Phys., Volume 16, 382-402 (2014).
Yanzhao Cao, and Song Chen, A computational model of steady bioconvective flow with concentration dependent viscosity, International Journal of Numerical Analysis and Modeling, Volume 11, no. 1 86-101, (2014).
Yanzhao Cao, Song Chen, and A.J. Meir.
On steady flow in a poroelastic porous medium, Mathematical
Method in Applied Sciences, Vol. 37-7 1029-1041
Xiaolong Hu, Xiaoming Wang,
Max Gunzburger, Fei Hua and Yanzhao Cao, Experimental and
computational validation and verification of the
Stokes-Darcy and continuum pipe flow models for karst
aquifers with dual porosity structure, Hydrological
Processes, Vol 26, 2031-2040 (2012).
Cao, X. He, M.
Gunzburger and X. Wang, Robin Robin domain decomposition
methods for the steady-state Stokes-Darcy system with the
Beavers Joseph interface condition, Numer. Math. Vol.
117, 601-629, (2011).
Cao and Li Yin,
Spectral method for nonlinear stochastic partial
differential equations of ellitpic type. Numer. Math.
Theor. Meth. Appl. Vol. 4, 38-52, (2011).
Weidong Zhao, Numerical solutions for forward backward
doubly stochastic partial differential equations and Zakai
equations, International Journal for Uncertainty
Quantification, 1 (4): 351--367, (2011).
Yanzhao Cao, Fei Hua, M. Gunzburger, Xiaoming Wang, Finite element approximations of pipe flow interface problems. Numeri. Meth. PDEs. Vol. 27, 5, 1242-1252, (2011).
Chi and Yanzhao Cao, Generating parallel random
sequences via parameterizing EICGs for heterogeneous
computing environments, Lecture Notes in Computer
Science Volume 6019, 409-417,
Gunzburger, F. Hua and X. Wang, Coupled Stokes-Darcy Model
with Beavers-Joseph Interface Boundary Condition, Comm.
Volume 8, Number 1, 1-25, (2010). PDF
Cao, Z. Chen
and Max Gunzburger, Finite element method approximation and
error estimates for stochastic Stokes equations,
Advances in Computational Mathe-
matics, Vol. 33, 215-230, (2010). PDF
Yanzhao Cao, Fei Hua, M. Gunzburger, Xiaoming Wang, and Weidong Zhao, Finite Element Approximations for Stokes--Darcy Flow with Beavers--Joseph Interface Conditions. SIAM J. Numer. Anal. 47 4239 (2010).
Yanzhao Cao, Bin Wu and Yuesheng Xu, A fast collocation method for solving stochastic integral equation SIAM J. Numer. Anal Vol. 47, No. 5, pp. 3744--3767, (2009).
K. Blayneh, Yanzhao Cao and Hee-Dae Kwon, On asymptotic analysis and numerical optimal control of vector born diseases, Discrete and Continuous Dynamical System B Volume 11, Number 3 (2009). PDF
Yanzhao Cao, Z. Chen and Max
Gunzburger, An ANOVA analysis for a class of partial
differential equations with uncertain boundary conditions,
, Int. J. Numer. Anal.& Model..
Volume 6, Number 2, Pages 256--273, (2009).
Yanzhao Cao, H. Chi, C. Milton and
W. Zhao, Exploitation of sensitivity derivatives
on quasi Monte Carlo simulations, Monte Carlo Methods
and Applications, Vol. 14, 269-279, (2008) .
Yanzhao Cao, Ran Zhang and Kai Zhang,
Finite Element and Discontinuous Galerkin Method for
Stochastic Helmholtz Equation in Two- and Three-Dimensions.
J. Comp. Math., 26, 702-715, (2008).
Yanzhao Cao, K. Zhang and R. Zhang, Finite Element Method and Discontinuous Galerkin Method for Stochastic Scattering Problem of Helmholtz Type, Potential Analysis, Volume 28, 301-319, (2008). PDF
Yanzhao Cao and Li Yin, A spectral finite element method for stochastic wave equations in one dimensional space, Comm. Pure & Appl. Anal. 6, 607 - 617, (2007).
Yanzhao Cao, M. Huang and Y. Xu, A hybrid collocation method for Fredholm integral equations with singular kernels, Appl. Numer. Math. 57, 549-561 (2007).
Yanzhao Cao, L. Yin and H. Yang, Finite element methods for semilinear elliptic stochastic partial differential equations, Numerische Mathematik, Vol. 106 , 2007 PDF
Yanzhao Cao, G. Cerezo and T. Herdman and J. Turi, Singularity expansion for a class of neutral delay equations, accepted by J. Integral Equations Appl. Vol 19, 13-32, (2007).
Yanzhao Cao, M. Y. Hussaini and H. Yang, Numerical optimization of radiated engine noise with uncertain wave numbers, Int. J. Numer. Anal.& Model. Vol. 4 No. 3-4 392--401, (2007).
Yanzhao Cao, M. Y. Hussaini and Hongtao Yang, Parameter identification for a noise radiation problem, Int. J. Numer. Anal.& Model. Vol. 4, Number 1, Pages 116--126, (2007).
Yanzhao Cao, On the rate of convergence of Wiener-Ito expansion for generalized random variables, Stochastics, , 78 (3), 179-187, (2006) PDF
Yanzhao Cao, M.Y. Hussaini, T. Zang and A. Zetazalo, A variance reduction method using high order sensitivity derivatives, Appl. Numer. Math, 56, 800--813 (2006).
S. Wang, Yanzhao Cao and P. Rikvold, First-principles calculations for the adsorption of water molecules on the Cu(100) surface, Physics Review B Vol. 70, 205410 (2004).
Yanzhao Cao, M.Y. Hussaini and T. Zang, Applications of sensitivity in Monte Carlo simulation. AIAA Journal, Vol. 42, No. 4, 815-822 (2004). PDF
Yanzhao Cao, M. Y. Hussaini and T. Zang, On the exploitation of sensitivity derivatives for accelerating sampling methods for uncertainty analysis, AIAA paper 2003-1656, (2003).
Yanzhao Cao, M. Y. Hussaini and T. Zang, An efficient Monte Carlo method for optimal control problems with uncertainty, Computational Optimization and Applications, Vol. 26, 219-230, (2003). PDF
Yanzhao Cao, T. Herdman and Y. Xu, A hybrid collocation method for Volterra integral equations with weakly singular kernels. SIAM J. Numer. Anal., Vol. 41, No. 1, 364-381 (2003).
Yanzhao Cao and D. Stanescu, Shape optimization for noise radiation problems, Comp. & Math. Appl., Vol. 44, No. 12, 1539-1556, (2002).PDF
Yanzhao Cao, On convergence of optimal control problem to exact control problem for systems governed by Navier-Stokes equations (with M. Y. Hussaini), Proceedings of ICNPPA-2000, Vol 1, 117-126 (2001).
Yanzhao Cao, Numerical approximations of exact controllability problems using optimal control problems for parabolic differential equations, Appl. Math. Comp., Vol 119, 127-145, (2001).
Yanzhao Cao, Numerical solution of diffraction problems by a least-square finite element method (with H. Yang and G. Bao), Math. Meth. Appl. Sci. Vol. 23, 1073-1092 (2000).
Yanzhao Cao, On exact controllability and convergence of optimal controls to exact controls of parabolic equations, (with M. Gunzburger and and J.Turner) Optimal Control: Theory, Algorithms, and Applications, Kluwer, 67-83, (1999).
Yanzhao Cao, A nonconforming least squares finite element method for interface problems, (with M. Gunzburger) SIAM J. Numer. Anal. Vol 36, No. 2, 312-322 (1998).
Yanzhao Cao, On conditions of controllability for systems governed by parabolic differential equations, (with M. Gunzburger), Math. Anal. Appl., Vol. 215, 174-189 (1997).
Yanzhao Cao, Singularity preserving Galerkin methods for weakly singular Fredholm integral equations, (with Y. Xu) J. Integral Equations Appl., Vol. 6, 303-334 (1994).
Yanzhao Cao, On finite element approximations for the bifurcation solutions of free convention problems (with M. Huang), Proceedings on numerical methods for partial differential equations, (refereed), World Scientific, Singapore, 3-14 (1992).
Feng Bao, Yanzhao Cao, A. J. Mier, and Weidong Zhao, A first order scheme for backward doubly stochastic differential Equations, submitted to SIAM Journal on Uncertainty Quantification (2014) PDF