Purdue University

West Lafayette, IN 47907

Office: 435 math building

M.S, Purdue University, 2006-2008

Ph.D, Purdue University, 2008-present

- 1. Adaptive finite element method for partial differential equations with discontinuous coefficients from physics in 3D
- - The design and analysis of the a posteriori error estimation technique
- - Adaptive mesh refining procedure
- 2. Construction of finite element spaces and efficient matrix assembly
- - Hierarchical differential form basis on simplex (Nédélec first and second kinds, Raviart-Thomas, Brezzi-Douglas-Marini)
- - Finite element exterior calculus in 4D spacetime mesh
- - Canonical construction of nonconforming finite element spaces based on exterior calculus
- - Symmetric composite element for stress tensor
- 3. Spacetime Discontinuous Galerkin finite element methods for hyperbolic conservation laws

I am starting to work on two near future projects:

- The a posteriori error analysis for the Helmholtz type problem arising from time-harmonic Maxwell's equations \(\nabla\times (\mu^{-1} \nabla\times \boldsymbol{u}) + (i\omega \sigma- \omega^2 \epsilon) \boldsymbol{u} = \boldsymbol{f}\), and the more difficult case while \(\sigma=0 \).
- The well-posedness, the finite element method, and error analysis for the model problem arising from Magnetohydrodynamics (MHD), while magneto-convection (a first order convective term) is present: \(\nabla\times (\alpha \nabla\times \boldsymbol{B}) + \nabla\times(\boldsymbol{v}\times \boldsymbol{B}) + \gamma \boldsymbol{B} = \boldsymbol{f}\).

2010-2011. Meritorious contributor to Problem of the Week column at Purdue Mathematics

2009-2010. Excellence in Teaching Award as a graduate instructor, Department of Mathematics, Purdue University

2006. Meritorious winners ranking 19th/835 in US Mathematical Contest in Modeling (COMAP)

- (with Zhiqiang Cai) Recovery-Based A Posteriori Error
Estimators
for \(\boldsymbol{H}(\mathbf{curl})\)-Interface Problems, submitted

- (with Zhiqiang Cai) Two New A Posteriori Error Estimators For
Nédélec finite elements in \(\boldsymbol{H}(\mathbf{curl})\)-Problem,
to be submitted

- (with Zhiqiang Cai, and Rob Falgout) A Posteriori Error Estimation for Finite Element Approximation to \(\boldsymbol{H}(\mathbf{curl})\)-Problems, to be submitted
- A Discrete de Rham Complex for Discontinuous Functions on Stars, unpublished
- A Canonical Construction of Nonconforming Vector Finite Elements based on de Rham Complex, unpublished

- CSESC, April 2013, Purdue University: Adaptive Finite Element Methods for Maxwell’s Equations
- Center of Computational and Applied Math lunch seminar, October 2013, Purdue University: How to Construct A Posterori Error Estimators for Time-domain Maxwell’s Equations with Discontinuous Coefficients
- Finite Element Circus, October 2013, University of Delaware: A Posteriori Error Estimation for H(curl)-Interface Problems

Fall 2013: Instructor, MA224 Business Calculus II, Distant Learning Online section

Summer 2013: Instructor/Course coordinator, MA266 Ordinary Differential Equations

Summer 2012: Instructor/Course coordinator, MA266 Ordinary Differential Equations

Fall 2011: Instructor, MA223 Business Calculus I

Summer 2010: Instructor, MA266 Ordinary Differential Equations

Spring 2010: Instructor, MA223 Business Calculus I

Fall 2009: Instructor, MA153 Algebra And Trigonometry I

Summer 2009: Instructor, MA162 Calculus II

Fall 2008: Instructor, MA153 Algebra And Trigonometry I

Summer 2008: Instructor, MA162 Calculus II

Spring 2008: Recitation TA, MA161 Calculus I

Fall 2007: Recitation TA, MA262 Linear Algebra and Differential Equations I

Spring 2007: Recitation TA, MA173 Honor Calculus II

5K | 22m47s |

10K | 48m46s |

Half-marathon | 1h55m |

Marathon | 4h18m |