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 and uncertainty quantification for deep learning.
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.
Jingshi Li, Song Chen, Yanzhao Cao, and Zhao Sun, A
neural network approach to sampling based learning control for
quantum system with uncertainty, accepted by Commun.
66. Lijin Wang, Yanzhao Cao, and Sau-Hai Lam, Explicit integration of stochastic fast-slow chemical reaction systems via an efficient implementation of stochastic computational singular perturbation, Communications in Computational Physics, 25(5), 1523-1546 (2019).
65. 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,
64. Jingyuan Zhang, Yanzhao Cao, and Hongxing Rui, A partitioned method with different time steps for coupled Stokes and Darcy flows with transport, International Journal of Numerical Analysis and Modeling, 163(2), 463-498 (2019).
63. 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,
Cao, 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).
61. 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).
60. 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).
59. 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).
55. Feng Bao,
Yanzhao Cao, Clayton Webster, and Guannan Zhang,
An efficient meshfree implicit filter for nonlinear filtering
problems, I. J. UQ, 6(1), 19-33 (2016).
53. Feng Bao, Yanzhao Cao,
A. J. Meir, and Weidong Zhao, A first order
scheme for backward doubly stochastic differential
equations, SIAM Journal on
Uncertainty Quantification, 4(1),
53. Yanzhao Cao and Dawit Denu, Analysis of stochastic vector-host epidemic model with direct transmission, DCDS-B, 21(7), 2109-2127 (2016).
52. 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).
51. 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).
Yanzhao 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).
49. 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)
47. 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).
45. 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).
44. 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)
43. 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).
Cao, 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).
41. 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).
40. 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).
39. 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
37. 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).
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).
and Li Yin, Spectral method for nonlinear stochastic partial
differential equations of ellitpic type. Numer. Math.
Theor. Meth. Appl. Vol. 4, 38-52, (2011).
Feng Bao, Yanzhao
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).
33. 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).
Hongmei Chi and Yanzhao Cao, Generating
parallel random sequences via parameterizing EICGs for
heterogeneous computing environments, Lecture Notes
in Computer Science Volume 6019,
M. Gunzburger, F. Hua and X. Wang, Coupled Stokes-Darcy
Model with Beavers-Joseph Interface Boundary Condition, Comm.
Math. Sci., Volume 8, Number 1,
1-25, (2010). PDF
Z. Chen and Max Gunzburger, Finite element method
approximation and error estimates for stochastic Stokes
equations, Advances in Computational
matics, Vol. 33, 215-230, (2010). PDF
29. 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).
28. 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).
27. 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
26. 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).
25. 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) .
24. 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).
23. 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
22. 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).
21. 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).
20. Yanzhao Cao, L. Yin and H. Yang, Finite element methods for semilinear elliptic stochastic partial differential equations, Numerische Mathematik, Vol. 106 , 2007 PDF
19. 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).
18. 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).
17. 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).
16. Yanzhao Cao, On the rate of convergence of Wiener-Ito expansion for generalized random variables, Stochastics, , 78 (3), 179-187, (2006) PDF
15. 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).
14. 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).
13. 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
12. 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).
11. 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
10. 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).
9. Yanzhao Cao and D. Stanescu, Shape optimization for noise radiation problems, Comp. & Math. Appl., Vol. 44, No. 12, 1539-1556, (2002).PDF
8. 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).
7. Yanzhao Cao, Numerical approximations of exact controllability problems using optimal control problems for parabolic differential equations, Appl. Math. Comp., Vol 119, 127-145, (2001).
6. 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).
5. 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).
4. 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).
3. Yanzhao Cao, On conditions of controllability for systems governed by parabolic differential equations, (with M. Gunzburger), Math. Anal. Appl., Vol. 215, 174-189 (1997).
2. Yanzhao Cao, Singularity preserving Galerkin methods for weakly singular Fredholm integral equations, (with Y. Xu) J. Integral Equations Appl., Vol. 6, 303-334 (1994).
1. 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).