Immersed boundary smooth extension: A high-order method for solving PDE on arbitrary smooth domains using Fourier spectral methods. - David B. Stein; Robert D. Guy; Becca Thomases (J. Comput. Phys., 2016)

Immersed Boundary Smooth Extension (IBSE): A high-order method for solving incompressible flows in arbitrary smooth domains. - David B. Stein; Robert D. Guy; Becca Thomases (J. Comput. Phys., 2017)

A stable and accurate scheme for solving the Stefan problem coupled with natural convection using the Immersed Boundary Smooth Extension method. - Jinzi Mac Huang; Michael J. Shelley; David B. Stein (J. Comput. Phys., 2021)

Quadrature by fundamental solutions: kernel-independent layer potential evaluation for large collections of simple objects. - David B. Stein; Alex H. Barnett (Adv. Comput. Math., 2022)

Spectrally accurate solutions to inhomogeneous elliptic PDE in smooth geometries using function intension. - David B. Stein (J. Comput. Phys., 2022)

A fast Chebyshev method for the Bingham closure with application to active nematic suspensions. - Scott Weady; Michael J. Shelley; David B. Stein (J. Comput. Phys., 2022)

A fully adaptive, high-order, fast Poisson solver for complex two-dimensional geometries. - Daniel Fortunato; David B. Stein; Alex H. Barnett (CoRR, 2025)