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
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.
4. Yuehseng Xu,
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.
9. Hongmei Chi, FAMU, Efficient quasi-Monte Carlo method
10. Hae-Dee Kwon,
11. Kbnesh Blayneh, FAMU, vector born
disease
PUBLICATIONS
Yanzhao Cao and Li Yin, A
spectral finite element method for stochastic elliptic
equations in two dimensional space, to
appear.
Yanzhao Cao, Z. Chen and Max Gunzburger, An ANOVA analysis for a class of partial
differential equations with uncertain boundary conditions, to appear. .
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
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.
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)
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,