Penn State University  
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Contact:
Email: tian@math.psu.edu
Address: Department of Mathematics
  Penn State University
  State College, PA 16801
  USA
Office: 217 McAllister
Telephone: (814)863-9052
   
Educational Background:
2009-2012:
 Chowla Research Assistant Professor, Penn State University, USA.
2005-2009:
 Ph.D. of Mathematics, University of South Carolina, USA.
2003-2006:
 M.S. of Mathematics, Shandong University, China.
1999-2003:
 B.S. of Mathematics, Shandong University, China.

Teaching:
Math 251, Sections 02 (Spring 2012)
Math 231 Section 06 and 11 (Fall 2011)
Math/CMPSC 451 Section 02 (Spring 2011)
Math 140 Section 020 & 037 (Fall 2010)
Math 141 Section 03 (Fall 2009)
Math 242 Section 5 (USC, Spring 2009)
Math 141 Section 501 Maple Lab (USC, Fall 2008)
Math 526 MATLAB Lab (USC, Fall 2008)
Math 526 MATLAB Lab (USC, Spring 2008)
Math 170 (USC, Fall 2007)
Math 526 Maple Lab (USC, Spring 2007)
Math E141 Maple Lab (USC, Spring 2007)
 
Research Interest:
Finite element/volume methods for PDEs.
Numerical Analysis.
Peridynamic theories.
Numerical methods for peridynamic and nonlocal models.
Spline finite element methods.
Numerical analysis of stochastic differential equations.

CV & Research Statement:
My CV
My Research Statement

Advisors:
Postdoc: Prof. Qiang Du, Penn State University, State College, PA, USA
Ph.D. : Prof. Lili Ju, University of South Carolina, Columbia, SC, USA
M.S. : Prof. Weidong Zhao, Shandong University, Jinan, China

Publications (My Erdos number is 3):
 
  • "A Convergent Adaptive Finite Element Method for Nonlocal Diffusion Model", submitted; with Q. Du and X. Zhao.
 
  • "A Posteriori Error Analysis of Finite Element Method for Linear Nonlocal Diffusion and Peridynamic Models", submitted; with Q. Du, L. Ju and K. Zhou.
  • "Optimal upwind control volumes for finite volume approximations of convection-diffusion equations",submitted; with L. Ju, X. Xiao and W.D. Zhao.
  • "Adaptive Finite Element Methods for Elliptic Equations over Hierarchical T-meshes", Journal of Computational and Applied Mathematics, Vol. 236, pp. 878-891, 2011; with F. Chen and Q. Du. [pdf]
  • "Finite element approximation of the Cahn-Hilliard equations on surfaces", Computer Methods in Applied Mechanics and Engineering, Vol. 200, pp. 2458-2470, 2011; with Q. Du and L. Ju. [pdf]
  • "A posteriori error estimates for finite-volume approximation of elliptic equations on general surfaces", Computer Methods in Applied Mechanics and Engineering, Vol. 198, pp. 716-726, 2009; with L. Ju and D. Wang. [pdf]
  • "Analysis of a mixed finite-volume discretization for fourth-order equations on general surfaces", IMA Journal of Numerical Analysis, Vol. 29, pp. 376-403, 2008; with Q. Du and L. Ju. [pdf]
  • "Convergence analysis of a splitting method for stochastic differential equations", International Journal of Numerical Analysis and Modeling, Vol. 5, pp. 673-692, 2008; with L. Ju and W.D. Zhao. [pdf]
  • "Numerical simulations of the steady Navier-Stokes equations using adaptive meshing schemes", International Journal for Numerical Methods in Fluids, Vol. 56, pp. 703-721, 2008; with L. Ju and H.-C. Lee. [pdf]
 

Talks:
 
  • "A Posteriori Error Analysis of Finite Element Method for Linear Nonlocal Diffusion and Peridynamic Models", 2011 International Congress of Industrial and Applied Mathematics, Vancouver, BC, Canada, July 18 - 22, 2011.
  • "A Posteriori Error Analysis of Finite Element Method for Linear Nonlocal Diffusion and Peridynamic Models", 2011 International Conference on Applied Mathematics and Interdisciplinary Research, Nankai University, Tianjian, China, June 13-16, 2011.
  • "Adaptive Finite Element Methods for Elliptic Equations over Hierarchical T-meshes", "A Posteriori Error Analysis of Finite Element Method for Linear Nonlocal Diffusion and Peridynamic Models",Department of Mathematics, Shandong University, Jinan, Shandong, China, June 2011.
 
  • "Adaptive Finite Element Methods for Elliptic Equations over Hierarchical T-meshes", Department of Scientific Computing, Florida State University, Tallahassee, FL, March 16, 2011.
  • "Adaptive Finite Element Methods for Elliptic Equations over Hierarchical T-meshes", SIAM ANNUAL 2010, Pittsburgh, PA, July 12-16, 2010.
  • "Adaptive Finite Element Methods for Elliptic Equations over Hierarchical T-meshes", 34th
    16th US National Congress of Theoretical and Applied Mechanics, State College, PA, June 27 - July 2, 2010.
  • "Adaptive Finite Element Methods for Elliptic Equations over Hierarchical T-meshes", 34th
    SIAM Southeastern-Atlantic Section Annual Meeting, Raleigh, NC, March 20-21, 2010.
  • "Analysis of a mixed finite-volume discretization of fourth order equations on general surfaces", 33rd
    SIAM Southeastern-Atlantic Section Annual Meeting, Columbia, SC, April, 2009.
  • "Analysis of a mixed finite-volume discretization of fourth order equations on general surfaces", SIAM Conference on Computational Science and Engineering, 2009, Miami, FL, March 2-6, 2009.
  • "A posteriori error estimates for finite-volume approximation of elliptic equations on general sur
    faces"    , SIAM Annual Meeting 2008, (Student Day's presentation), San Diego, CA, July, 2008.
  • "Analysis of a mixed finite-volume discretization of fourth order equations on general surfaces", 32nd
    SIAM Southeastern-Atlantic Section Annual Meeting, Orlando, FL, March, 2008.
  • "Analysis of a mixed finite-volume discretization of fourth-order equations on general surfaces",
    Cha-Cha Days Workshop 2007, Hampton, VA, October, 2007.
  • ACES Workshop 2006, Emory University, Atlanta, GA, November, 2006.
 
Awards:
 
 
  • Outstanding Graduate Student, University of South Carolina, Columbia, SC, 2009.