Samuel E. Reynolds

• Portland, Oregon
• Email: [email protected]
• Website: https://samreynoldsmath.xyz
• GitHub: https://github.com/samreynoldsmath

Summary

Computational mathematician with expertise in scientific computing, numerical methods, and optimization. Experienced in building and contributing to open-source research software, collaborating on peer-reviewed publications, and teaching at the university level. Skilled in developing numerical algorithms and scientific software to solve computational problems.

Skills

• PDE solvers (NGSolve, PETSc, MFEM, PuncturedFEM)
• Mesh generation and processing
• Numerical linear algebra
• Numerical optimization
• Integral equations
• Data clustering
• HPC and parallel computing
• Scientific Python stack (NumPy, SciPy, Matplotlib, Pandas, Jupyter)
• Linux development environment
• Languages: Python, C, C++, MATLAB
• Software: Bash, Git, LaTeX, Wolfram Mathematica

Education

Ph.D. in Mathematical Sciences

• Portland State University
• June 2024
• Advisor: Jeffrey S. Ovall
• Dissertation: H¹-conforming Finite Elements on Nonstandard Meshes

M.S. in Mathematics

• Portland State University
• April 2020

B.S. in Mathematics

• Portland State University
• August 2017
• Minor in Physics; magna cum laude; departmental honors.

Work Experience

Artificial Intelligence Trainer

• Data Annotation (Remote)
• April 2025 – Present
• Developed and reviewed mathematical reasoning tasks for training next-generation language models.
• Verified solutions and proofs, and documented model reasoning failures.
• Peer-reviewed prompt submissions for accuracy and clarity.

Computational Mathematics Research Assistant

• Fariborz Maseeh Dept. of Math. and Stats., Portland State University (Portland, Oregon)
• June 2016 – June 2024
• Designed and implemented finite element methods incorporating mesh cells with cavities and curved edges.
• Coauthored four peer-reviewed publications on the analysis and implementation of these methods.
• Created, documented, and released the PuncturedFEM Python package (PyPI) for computational experiments and reproducible research.
• Contributed to convex optimization research for clustering problems, resulting in two additional peer-reviewed publications.

Computing Scholar (Summer Internship)

• Lawrence Livermore National Laboratory (Remote)
• June 2022 – August 2022
• Built numerical examples and simulations using MFEM (a C++ library for partial differential equations).
• Demonstrated multi-physics modeling techniques in a HPC environment.

Givens Associate (Summer Internship)

• Argonne National Laboratory (Remote)
• June 2021 – August 2021
• Contributed to the PETSc open-source codebase (a C library for scientific computing).
• Implemented high-performance algorithms for parallel matrix computations.

Graduate Teaching Assistant

• Fariborz Maseeh Dept. of Math. and Stats., Portland State University (Portland, Oregon)
• September 2019 – December 2020
• Gave lectures, prepared course materials, graded student work, and mentored students during office hours.
• Total of four courses taught (Calculus I, Calculus IV), two of which were held remotely.

Peer Tutor

• The Learning Center, Portland State University (Portland, Oregon)
• April 2016 – August 2019
• Assisted undergraduate students in drop-in one-on-one sessions.
• Subjects: elementary algebra, calculus, differential equations, linear algebra, introductory physics.

MTH 251 Lab Assistant

• Mathematics Department, Portland Community College (Portland, Oregon)
• April 2015 – March 2016
• Assisted students with introductory calculus during in-class workshop sessions.

Publications

1. Jeffrey S. Ovall and Samuel E. Reynolds. “Evaluation of Inner Products of Implicitly Defined Finite Element Functions on Multiply Connected Planar Mesh Cells.” SIAM Journal on Scientific Computing 46.1 (2024), A338–A359.
2. Jeffrey S. Ovall and Samuel E. Reynolds. “Quadrature for implicitly-defined finite element functions on curvilinear polygons.” Computers & Mathematics with Applications 107 (2022), 1–16.
3. Akash Anand et al. “Trefftz finite elements on curvilinear polygons.” SIAM Journal on Scientific Computing 42.2 (2020), A1289–A1316.
4. Nguyen Mau Nam et al. “Clustering and multifacility location with constraints via distance function penalty methods and DC programming.” Optimization 67.11 (2018), 1869–1894.
5. Nguyen Mau Nam et al. “Nesterov’s smoothing technique and minimizing differences of convex functions for hierarchical clustering.” Optimization Letters 12 (2018), 455–473.
6. Jeffrey S. Ovall and Samuel E. Reynolds. “A high-order method for evaluating derivatives of harmonic functions in planar domains.” SIAM Journal on Scientific Computing 40.3 (2018), A1915–A1935.

Awards, Honors, and Certifications

• NSF Research Training Group Graduate Fellowship, National Science Foundation (2022, 2023)
• Excellence in Remote Teaching Award, PSU Fariborz Maseeh Dept. of Mathematics and Statistics (2020)
• Level III (Master) Tutor Certification, College Reading & Learning Association (2019)
• F. S. Cater Prize, PSU Fariborz Maseeh Dept. of Mathematics and Statistics (2019)
• Christine and David Vernier STEM Scholarship, PSU College of Liberal Arts and Sciences (2016)
• Oregon NASA Space Scholarship, Oregon Space Grant Consortium (2015)