Danielle Maddix
Ph.D. Student in Computational and Mathematical Engineering, admitted Autumn 2013
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 (20122014) 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 (20162017)

Graduate Research Fellowship Program, National Science Foundation (20132016)

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 (20082012)

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)
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, PostDoc, 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, PostDoc, Lawrence Berkeley National Laboratory
For More Information:
201718 Courses
 Advanced MATLAB for Scientific Computing
CME 292 (Aut, Spr) 
Prior Year Courses
201617 Courses
 Advanced MATLAB for Scientific Computing
CME 292 (Aut, Spr)
 Advanced MATLAB for Scientific Computing
Work Experience

LargeScale 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 oneday 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

Numerical Artifacts in the Generalized Porous Medium Equation: Why Harmonic Averaging Itself Is Not to Blame
Journal of Computational Physics
2018; 361 (C): 280298
View details for DOI 10.1016/j.jcp.2018.02.010
 Numerical Artifacts in the Discontinuous Generalized Porous Medium Equation: How to Avoid Spurious Temporal Oscillations Submitted, Journal of Computational Physics 2018; arXiv:1712.00132
 Advanced Fluid Reduced Order Models for Compressible Flow Sandia National Laboratory. Albuquerque, NM. 2017 ; Sandia Laboratories Report (Sand No. 201710335): http://www.sandia.gov/~ikalash/FY17_SAND_report.pdf
 MINRES: Sparse Symmetric Equations Systems Optimization Laboratory (SOL). 2015