RESEARCH AND PREPRINTS

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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 noise radiation problems related aircraft engines, and optimal controls of mathematical biology problems such as vector born diseases.


Current projects:

1. Modeling and numerical simulations for flows in karest aquifers.
2. Numerical solutions for stochastic parabolic partial differential equations.
3. Finite element approximation for stochastic Stokes equations.
4. Fast collocation method for stochastic Fredholm integral equations.
5. Optimal control of vector born disease model.
   
   
Recent and current Collaborators
      
1. Max Gunzburger, FSU,stochastic partial differential equations, flow in porous media
2. M. Y. Hussaini, FSU, Monte Carlo method for optimal control problems under uncertainty
3. Terry Herdman, Virginia Tech, numerical solutions for integral delay equations
4. Yuehseng Xu,   Syracuse University, stochastic integral equations
5. Xiaoming Wang,  FSU, flow in porous media
6. Hongtao Yang,   UNLV, Optimal control for noise radiation problems, numerical SPDEs
7. Bin Wu, Zhongshan Unviersity, stochastic integral equations
8. Li Yin, Jilin University, stochastic partial differential equations
9. Hongmei Chi, FAMU, Efficient quasi-Monte Carlo method
10. Hae-Dee Kwon, Ihan University, vector born disease control
11. Kbnesh Blayneh, FAMU, vector born disease

PUBLICATIONS

 

 


Yanzhao Cao, Z. Chen and Max Gunzburger, Finite element method approximation and
error estimates for stochastic Stokes equations, accepted by  Advances in Computational Mathe-
matics,  PDF

 

Yanzhao Cao, M. Gunzburger, F. Hua and X. Wang, Coupled Stokes-Darcy Model with Beavers-Joseph Interface Boundary Condition, accepted by  Comm. Math. Sci., PDF

 

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, May 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, accpeted by 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,  accepted by   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)
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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.