Tristan Goodwill
Research interests
Numerical analysis, fast algorithms, analysis of PDEs in mathematical physics
Education
Ph. D. in Mathematics
Courant Institute of Mathematical Sciences, New York University — 2017–2023
On the solution of elliptic partial differential equations on surfaces: Regularity and numerical approaches
Adviser: Michael O’Neil
B. Sc.
McMaster University — 2013–2017
Honours Integrated Science (Physics) with a minor in Mathematics
Employment
William H. Kruskal Instructor
Committee on Computational and Applied Mathematics, University of Chicago — 2023–Present
Teaching Assistant
Courant Institute of Mathematical Sciences, New York University — Spring and Fall 2019, Fall 2021, Spring 2022
Papers
Goodwill, T., Jiang, S., Rachh, M., Sugita, K. A domain decomposition method for computing the scattering matrix of waveguide circuits. Preprint arXiv 2509.20695
Goodwill, T., Greengard, L., Hoskins, J., Rachh, M, and Wang, Y. Fast multipole method with complex coordinates. Preprint arXiv 2509.05458
Agocs, F., Goodwill, T. and Hoskins, J. Complex scaling for the junction of semi-infinite gratings. Preprint arXiv 2509.02951
Epstein, C., Goodwill, T., Hoskins, J., Quinn, S. and Rachh, M. Complex scaling for open waveguides. Preprint arXiv 2506.10263
Goodwill, T. and Epstein, C. A numerical method for scattering problems with unbounded interfaces. Preprint arXiv 2411.11204
Goodwill, T. and O’Neil, M. A parametrix method for elliptic surface PDEs. Pure and Applied Analysis 7(1), 2025.
Goodwill, T. and O’Neil, M. An interface formulation of the Laplace-Beltrami problem on piecewise smooth surfaces. SIAM Journal on Mathematical Analysis 55(6), 2023.
Li, H., Goodwill, T., Wang, Z. J., and Ristroph, L. Centre of mass location, flight modes, stability and dynamic modelling of gliders. Journal of Fluid Mechanics, 937, 2022.
Morsy-Osman, M., Sowailem, M., El-Fiky, E., Goodwill, T., Hoang, T., Lessard, S., and Plant, D. V. DSP-free coherent-lite transceiver for next generation single wavelength optical intra-datacenter interconnects. Optics Express, 26(7), 2018.
Software development
ChunkIE A Matlab integral equation toolbox — March 2024–Present
fmm3dbie — June 2024–Present
Teaching
CAAM 37830 Scientific Computing with Python — Autumn 2023, Autumn 2024, Autumn 2025
Master’s level, Committee on Computational and Applied Mathematics, University of Chicago
MATH 21100 Basic Numerical Analysis — Spring 2024, Spring 2025
Undergraduate level, Department of Mathematics, University of Chicago
CAAM 31110 Integral Equation Methods for PDEs — Winter 2025
PhD topics course, Committee on Computational and Applied Mathematics, University of Chicago
Awards and other experience
AMS-Simons Travel Grant — July, 2025 –June 2027
Numerical PDEs: Analysis, Algorithms, and Data Challenges — January–March 2024
Semester workshop — ICERM, Providence
Best poster award — March 2, 2023
SIAM CSE 2023 — RAI Congress Center, Amsterdam
SIAM Student Travel Award — July 11, 2022
SIAM Annual Meeting 2022 — David L. Lawrence Convention Center, Pittsburgh, Pennsylvania
Organized Minisymposia
Recent Advances in Fast and Accurate Methods for Wave Problems — July 14, 2025
with Nour Al Hassanieh, Flatiron Institute — ICOSAHOM 2025 — McGill University
Recent Advances in Integral Equation Methods and Their Applications — March 5, 2025
with Felipe Vico, Universidad Politecnica de Valencia — SIAM CSE 2025 — Fort Worth Convention Center
Talks
A fast integral equation method for PDEs on surfaces — July 29, 2025
12th Applied Inverse Problems Conference — FGV EMAp, Brazil
Complex scattering makes for simple numerics: A method for simulating junctions of several semi-infinite domains — July 14, 2025
ICOSAHOM 2025 — McGill University
Complex scattering makes for simple numerics — June 11, 2025
CCM Colloquium — Flatiron Institute
Complex scattering makes for simple numerics — March 5, 2025
SIAM CSE 2025 — Fort Worth Convention Center
Complex scattering makes for simple numerics — February 6, 2025
Computational and Applied Math Colloquium — Committee on Computational and Applied Mathematics, University of Chicago
A fast integral equation solver for surface PDEs — July 15, 2024
SciCADE 2024 — National University of Singapore
A fast integral equation solver for surface PDEs — March 12, 2024
Semester Program: Numerical PDEs: Analysis, Algorithms, and Data Challenges — ICERM, Brown University
A fast integral equation solver for surface PDEs — December 1, 2023
International Workshop on “Vector- and Tensor-Valued Surface PDEs” — TU Dresden
Integral methods for surface PDES — August 17, 2023
ICOSAHOM 2023 — Yonsei University
Integral methods for surface PDES — April 26, 2023
Applied Mathematics Seminar — Yale University