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
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, DOI: 10.1002/hyp.8308, 2011.
Yanzhao 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.
Yanzhao 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.
Feng Bao, Yanzhao Cao, and 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.
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)
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, accepted 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)
.
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.