An efficient method for the incompressible Navier-Stokes equations on irregular domains with no-slip boundary conditions, high order up to the boundary. - David Shirokoff; Rodolfo Ruben Rosales (J. Comput. Phys., 2011)

Sufficient Conditions for Global Minimality of Metastable States in a Class of Non-convex Functionals: A Simple Approach Via Quadratic Lower Bounds. - David Shirokoff; Rustum Choksi; Jean-Christophe Nave (J. Nonlinear Sci., 2015)

A Sharp-Interface Active Penalty Method for the Incompressible Navier-Stokes Equations. - David Shirokoff; Jean-Christophe Nave (J. Sci. Comput., 2015)

A Fourier penalty method for solving the time-dependent Maxwell's equations in domains with curved boundaries. - Ryan Galagusz; David Shirokoff; Jean-Christophe Nave (J. Comput. Phys., 2016)

Unconditional Stability for Multistep ImEx Schemes: Theory. - Rodolfo Ruben Rosales; Benjamin Seibold; David Shirokoff; Dong Zhou (SIAM J. Numer. Anal., 2017)

Approximate Global Minimizers to Pairwise Interaction Problems via Convex Relaxation. - Mahdi Bandegi; David Shirokoff (SIAM J. Appl. Dyn. Syst., 2018)

Unconditional stability for multistep ImEx schemes: Practice. - Benjamin Seibold; David Shirokoff; Dong Zhou (J. Comput. Phys., 2019)

High-order Methods for a Pressure Poisson Equation Reformulation of the Navier-Stokes Equations with Electric Boundary Conditions. - Rodolfo Ruben Rosales; Benjamin Seibold; David Shirokoff; Dong Zhou (CoRR, 2020)

Design of DIRK Schemes with High Weak Stage Order. - Abhijit Biswas; David I. Ketcheson; Benjamin Seibold; David Shirokoff (CoRR, 2022)

Explicit Runge Kutta Methods that Alleviate Order Reduction. - Abhijit Biswas; David I. Ketcheson; Steven Roberts; Benjamin Seibold; David Shirokoff (CoRR, 2023)

Algebraic Conditions for Stability in Runge-Kutta Methods and Their Certification via Semidefinite Programming. - Austin Juhl; David Shirokoff (CoRR, 2024)

Algebraic Structure of the Weak Stage Order Conditions for Runge-Kutta Methods. - Abhijit Biswas; David I. Ketcheson; Benjamin Seibold; David Shirokoff (SIAM J. Numer. Anal., 2024)

Convergence of Markov Chains for Constant Step-Size Stochastic Gradient Descent with Separable Functions. - David Shirokoff; Philip Zaleski (SIAM J. Appl. Dyn. Syst., 2025)

Explicit Runge-Kutta Methods that Alleviate Order Reduction. - Abhijit Biswas; David I. Ketcheson; Steven B. Roberts; Benjamin Seibold; David Shirokoff (SIAM J. Numer. Anal., 2025)

Runge-Kutta Methods and Stiff Order Conditions for Semilinear ODEs. - Steven B. Roberts; David Shirokoff; Abhijit Biswas; Benjamin Seibold (CoRR, 2025)

Preconditioning and Linearly Implicit Time Integration for the Serre-Green-Naghdi Equations. - Linwan Feng; David Shirokoff; Wooyoung Choi (CoRR, 2025)