Research Interests
My primary research area is numerical analysis. More specifically, I am interested in the numerical solution of partial differential equations that arise in real-world applications. Over the last several years, I have carried out research on problems from financial mathematics, contact mechanics and biomedical imaging. Following is the list of papers I have coauthored.
Publications
Contact Mechanics
- Numerical Analysis of History-Dependent Quasivariational Inequalities with Applications in Contact Mechanics.
With M. Barboteu, W. Han, and M. Sofonea, ESAIM: Mathematical Modelling and Numerical Analysis, Accepted, 2013. - Analysis of a dynamic electro-elastic problem.
With M. Barboteu, M. Sofonea, and W. Han, ZAMM - Journal of Applied Mathematics and Mechanics, Vol. 93, 612-632, 2013. - Analysis and Numerical Solution of a Piezoelectric Frictional Contact Problem.
With M. Sofonea, M. Barboteu, and W. Han, Applied Mathematical Modelling, Vol. 36, 4483-4501, 2012.- Analysis and numerical solution of a frictionless contact problem for electro-elastic-visco-plastic materials.
With W. Han and M. Sofonea, Computer Methods in Applied Mechanics and Engineering, Vol. 196, 3915-3926, 2007.- An internal approximation of obstacle problems.
With W. Han, Bull. Math. Soc. Sc. Math. Roumaine, Vol. 48, 199-210, 2005. - Analysis and numerical solution of a frictionless contact problem for electro-elastic-visco-plastic materials.
Biomedical Imaging
- Studies of a mathematical model for temperature-modulated bioluminescence
tomography.
With W. Han, H. Shen, W. Cong, and G. Wang, Applicable Analysis, Vol. 88, 193-213, 2009. - An integrated solution and analysis of bioluminescence tomography and diffuse optical tomography.
With W. Han, W. Cong, and G. Wang, Communications in Numerical Methods in Engineering, Vol. 25, 639-656, 2009. - Bioluminescence tomography with optimized optical parameters.
With W. Han, W. Cong, and G. Wang, Inverse Problems, Vol. 23, 1215-1228, 2007. Financial Mathematics
- Adaptive θ-methods for pricing American options.
With A.Q.M. Khaliq and D.A. Voss, Journal of Computational and Applied Mathematics, Vol. 222, 210-227, 2008. - A linearly implicit predictor-corrector scheme for pricing American options using a penalty method approach.
With A.Q.M. Khaliq and D.A. Voss, Journal of Banking and Finance, Vol. 30, 489-502, 2006. - A fourth order L-stable method for the Black-Scholes model with barrier options.
With D.A. Voss, A.Q.M. Khaliq, and H. He, Lecture Notes in Computer Science, Springer-Verlag, Heidelberg, Vol. 2669, 199-207, 2003. Inverse Problems
- A numerical method for a Cauchy problem for elliptic partial differential equations.
With W. Han, J. Huang, and Y. Chen, Inverse Problems, Vol. 23, 2401-2415, 2007.