Bio


I am a PhD candidate in the Institute of Computational and Mathematical Engineering (ICME) at Stanford advised by Professor Margot Gerritsen. I have been funded by the NSF graduate research fellowship. I received my bachelor's degree in Applied Mathematics with highest honors from the University of California, Berkeley in 2012. I then continued onto my graduate education at ICME and earned my Masters in Computational and Mathematical Engineering in 2015. I have had internships in computational mathematics at the Lawrence Berkeley National Laboratory (2012-2014) and NVIDIA (2015). At the LBL, I worked in the Computational Research Division under Professor James Sethian, applying multiphase flow algorithms to shape optimization problems. At NVIDIA, I worked in the numerical linear algebra and graph analytics group. My current research is on developing new, accurate, stable and conservative numerical methods for mathematical modeling of ocean dynamics.

Honors & Awards


  • ICME Teaching Fellow, Stanford University (2017)
  • Graduate Voice and Influence Program (GVIP) Fellow, Stanford University (2016-2017)
  • Graduate Research Fellowship Program, National Science Foundation (2013-2016)
  • ICME Xpo Poster Presentation Award, Stanford University (May 2016)
  • Outstanding Graduate Student Instructor Award, University of California, Berkeley (March 2013)
  • Percy Lionel Davis Award for Excellence in Mathematics, University of California, Berkeley (May 2012)
  • Dean's List, University of California Berkeley (2008-2012)
  • Junior Initiate to Phi Beta Kappa Honor Society, University of California, Berkeley (2011)

Education & Certifications


  • MS, Stanford University, Computational and Mathematical Engineering (2015)
  • BA, University of California, Berkeley, Applied Mathematics (2012)

Stanford Advisors


Service, Volunteer and Community Work


  • Technology, Engineering and Mathematical Sciences Judge, Diocese of Oakland (2/1/2013 - Present)

    Interviewed aspiring young scientists in 7th and 8th grade about their science fair projects and encouraged young female students to become involved in STEM activities.

    Location

    Alameda, CA

  • Panel Member for Letters & Science, University of California, Berkeley (9/1/2011)

    Mentored incoming UC Berkeley freshmen about their STEM curriculum.

    Location

    Berkeley, CA

Current Research and Scholarly Interests


I develop advanced numerical methods for partial differential equations. We are investigating building a family of schemes which satisfy stability, accuracy and conservation properties for ocean dynamics. Of particular interest is conservation of enstrophy for vortices in ocean modeling using mimetic methods. I am advised by Professor Margot Gerritsen.

Projects


  • Thesis Research Project with Professor Margot Gerritsen, Stanford University (3/1/2016 - Present)

    Developing advanced and robust numerical methods for PDES, with applications to ocean dynamics and nonlinear heat equation. Implementing stable and accurate temporal and spatial discretizations for nonlinear equations.

    Location

    Stanford, CA

    Collaborators

    • Margot Gerritsen, Senior Associate Dean for Educational Initatives, Associate Professor of Energy Resources Engineering and, by courtesy, of Mechanical Engineering and of Civil and Environmental Engineering, Stanford University
    • Luiz Sampaio, Senior Physical Science Research Associate, Department of Energy Resources Engineering - Energy Resources Engineering, Department of Energy Resources Engineering - Energy Resources Engineering
    • Anna Nissen, Post-Doc, University of Bergen
  • Structure and Parameter Learning in Bayesian Networks with Applications to Predicting Breast Cancer Tumor Malignancy in Lower Dimension Feature Space (CS238 Final Project), Stanford University

    Utilized Bayesian Networks to determine the key features involved in diagnosing breast cancer malignancy.

    Location

    Stanford, CA

    For More Information:

  • Investigating the Effects of MINRES with Local Reorthogonalization (CME 338 Project), Stanford University (5/1/2015)

    Wrote optimized MATLAB version of numerical linear algebra iterative method, MINRES, with local reorthogonalization for the Systems Optimization Laboratory (SOL)

    Location

    Stanford, CA

    Collaborators

    • Michael Saunders, Professor (Research) of Management Science and Engineering, Stanford University

    For More Information:

  • Diagnosing Malignant versus Benign Breast Cancer Tumors Via Machine Learning Techniques in High Dimensions (CS 229 Project), Stanford University (12/1/2014)

    Implemented various supervised learning algorithms for this binary classification model involving breast cancer data from UC Irvine. Implemented Logistic regression, Linear and Quadratic Gaussian Discriminant Analysis (GDA), and Support Vector Machine (SVM) using 10 distinct continuous features.

    Location

    Stanford, CA

    Collaborators

    • Andrew Ng, Computer Science Professor, Stanford University

    For More Information:

  • Using Numerical Optimization Methods to find Hamiltonian Cycle in Directed Graph (CME 304 Project), Stanford University (3/1/2014)

    Used optimization formulation of relaxation of Hamiltonian Cycle in a Directed Graph Instance. Implemented using the Active Set Method and rounding to return discrete output.

    Location

    Stanford, CA

    Collaborators

    • Walter Murray, Professor (Research) of Management Science and Engineering, Emeritus, Stanford University

    For More Information:

  • Optimizations of Algorithms to Identify Strongly Connected Components in CUDA, Stanford University (5/1/2014)

    Implemented various kernels to identify strongly connected components in images in parallel on the GPU with performance testing.

    Location

    Stanford, CA

    Collaborators

    • Eric Darve, Associate Professor of Mechanical Engineering, Stanford University

    For More Information:

  • Applications of the Voronoi Implicit Interface Method for Shape Optimization Problems Involving Interconnected Regions, University of California, Berkeley (2012 - 2013)

    Applied the Voronoi Implicit Interface Method to shape optimization problems to find an optimal domain decomposition or grouping of clustered particles. The level set equation was solved to evolve boundaries of interconnected regions in time, subject to certain constraints and speed functions in two and three dimensions.

    Location

    Berkeley, CA

    Collaborators

    • James Sethian, Professor of Applied Mathematics, University of California, Berkeley
    • Robert Saye, Post-Doc, Lawrence Berkeley National Laboratory

    For More Information:

2017-18 Courses


Work Experience


  • Large-Scale Data Analytics Intern, Sandia National Laboratory (6/19/2017 - 9/21/2017)

    Developed structure preserving reduced order models (ROMs) for computationally expensive high fidelity models in computational fluid dynamics.

    Location

    Livermore, CA

  • ICME Data Science Summer Workshop Instructor and Organizer, ICME, Stanford University (8/1/2016)

    Taught one-day workshop to industry affliates and graduate students on the uses of Advanced MATLAB for Scientific Computing

    Location

    Stanford, CA

  • CUDA Software Engineer, NVIDIA (June 22, 2015 - September 11, 2015)

    I worked in the numerical linear algebra and graph analytics group to develop and implement efficient algorithms for sparse matrix vector multiplication on the GPU

    Location

    Santa Clara, CA

  • Computational Researcher, Lawrence Berkeley National Laboratory (May 2012 - September 2014)

    I worked in the Applied Math Group under Professor James Sethian on level set methods for computational fluid dynamics and on applying the Voronoi Implicit Interface Method (VIIM) for multiphase flow to shape optimization problems.

    Location

    Berkeley, CA

  • Numerical Linear Algebra Refresher Course, ICME, Stanford University (September 21, 2015 - September 24, 2015)

    Taught key components and background needed for core course CME 302 to incoming first year PhD and Master Students.

    Location

    Stanford, CA

  • Lecturer for Linear Algebra and Differential Equations, University of California, Berkeley (8/1/2012 - 12/1/2012)

    Taught Math 54 Section covering methods in linear algebra, ODEs and PDEs.

    Location

    Berkeley, CA

  • Teaching Assistant for Calculus (Math 1B and Math 16B), University of California, Berkeley (2011 - 2012)

    Taught a section of undergraduate second semester calculus, involving integration methods and differential equations.

    Location

    Berkeley, CA

All Publications


  • Advanced Fluid Reduced Order Models for Compressible Flow Tezaur, I., Fike, J., Carlberg, K., Barone, M., Maddix, D., Mussoni, E., Balajewicz, M. Sandia National Laboratory. Albuquerque, NM. 2017 ; Sandia Laboratories Report (Sand No. 2017-10335): http://www.sandia.gov/~ikalash/FY17_SAND_report.pdf
  • Numerical Artifacts in the Generalized Porous Medium Equation: Why Harmonic Averaging Itself Is Not to Blame Submitted, Journal of Computational Physics Maddix, D., Sampaio, L., Gerritsen, M. 2017; arXiv:1709.02581