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. 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. Accepted by Pure and Applied Analysis, 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

Awards and other experience

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

Talks

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