Graham Harper


My name is Graham Harper and I am a third-year Ph.D. candidate at Colorado State University in the department of Mathematics currently participating in the applied mathematics and dynamical systems track. I am actively researching novel finite element methods for elliptic PDEs in 3d. I have passed all my qualifying exams (Analysis, Linear Algebra, Partial Differential Equations, Numerical Analysis).


  • Colorado State University
    • PhD in Applied Mathematics expected May 2020. GPA: 3.937
  • Colorado State University - Pueblo
    • Graduated Summa Cum Laude May 2015 with a B.S. in Mathematics, and minors in industrial engineering, honors, and leadership studies. GPA: 3.994


  • Colorado State University Department of Mathematics
    • Graduate Research Assistant (Fall 2015 - Present)
  • Pacific Northwest National Lab - Computational Science and Mathematics Division
    • Graduate Student Fellow (Summer 2017)
    • Mentor: Dr. Bin Zheng
    • Funding from the NSF mathematical science graduate internship program
  • Colorado State University - Pueblo College of Science and Mathematics
    • Peer Tutor at the Math Learning Center (August 2012 July 2015)
    • Mathematics Department Grader (August 2013 May 2015)
    • College Algebra Recitation Leader (August 2013 May 2015)
    • Peer Tutor and Mentor at the PROPEL Center (August 2012 May 2015)

Relevant Coursework:

  • Advanced Numerical Methods for Solving Partial Differential Equations
  • Advanced Partial Differential Equations
  • Functional Analysis
  • Fundamentals of High Performance Computing
  • Industrial Mathematics

Teaching Experience:

  • Ordinary Differential Equations [MATH 340] Instructor (Fall 2017, Spring 2018)
  • Mathematical Algorithms I&II [MATH 151&152] Instructor (Spring 2017)
  • Calculus for Biological Scientists [MATH155] Instructor (Fall 2016)
  • Calculus for Physical Scientists [MATH160] Instructor (Fall 2015, Spring 2016)
  • Student Teacher for Mathematics at Centennial High School (Fall 2014) (CSU-Pueblo President's Leadership Program Capstone Project)
  • College Algebra [MATH121] Recitation Leader (Fall 2013 Spring 2015)

Strong Programming Experience:

  • Matlab (and its open-source clone Octave)
  • C++ (and parallel libraries OpenMP, MPI)
  • Java
  • Wolfram Mathematica
  • For specific programming projects, please view my github


  • Weak Galerkin finite element methods and applications to elliptic PDEs (including reduction and parallelization)
  • Contributed to the development of the DarcyLite+ C++ library
  • Contributed to LinLite C++ library
  • Developing a standalone library for solving finite volume flow problems in parallel as part of GRAD510


  • James Liu, Simon Tavener, Zhuoran Wang, Graham Harper. A 2-field Finite Element Solver for Poroelasticity on Triangular Meshes (In preparation).
  • James Liu, Simon Tavener, Graham Harper. Schur complement and parallelization of weak Galerkin finite element methods for 3-dim elliptic problems (In preparation).
  • Graham Harper, James Liu, Simon Tavener, Bin Zheng, Lowest-order weak Galerkin finite element methods for linear elasticity on rectangular and brick meshes (Submitted).
  • Graham Harper, James Liu, Bin Zheng. The THex algorithm and a simple Darcy solver on hexahedral meshes, Proc. Comput. Sci., 108C(2017), pp.1903--1912.


  • The Lowest-order Weak Galerkin Finite Element Method for Linear Elasticity SIAM CSS 2017. October 1, 2017.
  • The Lowest-order Weak Galerkin Finite Element Method for Linear Elasticity Pacific Northwest National Laboratory. August 8, 2017.
  • The Lowest Order Weak Galerkin Solver for the Darcy Equation on Hexahedral Meshes SIAM FRAMSC 2017. March 4, 2017.
  • Ebola, Equilibria, and Epidemiology: A Dynamical Analysis, Undergraduate Thesis Defense, Colorado State University - Pueblo, April 2015.
  • Noncollision Singularities in 5-Body Newtonian Systems, Independent Study Final Presentation, Colorado State University - Pueblo, April 2014.
  • A Visual Tour Through Chaos, Matlab Final Presentation, Colorado State University - Pueblo, April 2014. The final paper for the class is here

Conferences and Professional Memberships:

  • SIAM CSS 2017 (Fort Collins, CO)
  • CSU Greenslopes Seminar Co-Organizer (Spring 2017)
  • SIAM FRAMSC 2017 (Denver, CO)
  • SIAM Student Chapter Webmaster (2016 school year)
  • SIAM Annual Meeting 2016 (Boston, MA)
  • SIAM FRAMSC 2016 (Denver, CO)
  • SIAM Student Member (Fall 2015 - Present)
  • AMS Student Member (Fall 2014 - May 2015)
  • Lambda Chi Alpha brother from Delta Omega chapter. Served as High Sigma (Academic Chairman) for the Spring 2015 semester.
  • MAA MathFest 2014 (Portland, OR)
  • MAA MathFest 2013 (Hartford, CT)
  • MAA MathFest 2012 (Madison, WI)

Other Awards and Honors:

  • Received a score of 20 on the 2014 Putnam Exam (top 900 scores)
  • 2nd place at the US National Collegiate Mathematics Championship (August 2014, Portland, OR hosted by the ASCM and Dr. Richard Neal)
  • 4th place at the US National Collegiate Mathematics Championship (August 2013, Hartford, CT hosted by the ASCM and Dr. Richard Neal)
  • Outstanding Graduate Award (April 2015, Colorado State University - Pueblo Mathematics Department)
  • Threlkeld Prize for Excellence Finalist (April 2015, Colorado State University - Pueblo)

Location and Office Hours

Weber 230
Colorado State University
Fort Collins, CO 80521