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math.NA2026
A Butterfly-Accelerated Manifold Harmonic Transform
Paul G. Beckman, Samuel F. Potter, Michael O'Neil
The eigenfunctions of the Laplacian are a natural basis of functions for many tasks in computational mathematics. On the circle and sphere, the eigenfunctions are given by complex…
math.NA2025
Scattering theory for Stokes flow in complex branched structures
Haiyang Wang, Fredrik Fryklund, Samuel Potter +1
Slow, viscous flow in branched structures arises in many biological and engineering settings. Direct numerical simulation of flow in such complicated multi-scale geometry, however,…
math.NA2024
A Lightweight, Geometrically Flexible Fast Algorithm for the Evaluation of Layer and Volume Potentials
Fredrik Fryklund, Leslie Greengard, Shidong Jiang +1
Over the last two decades, several fast, robust, and high-order accurate methods have been developed for solving the Poisson equation in complicated geometry using potential theory…