Research

Philip Zaleski, Ph.D. Student
Department of Mathematical Sciences, NJIT

Austin Juhl, Ph.D., Summer 2024
Department of Mathematical Sciences, NJIT
Thesis: Certifying stability in Runge-Kutta schemes: Algebraic conditions and semidefinite programming

William (Joe) McCann, BS 2020, MS 2021, Summer 2021
Department of Mathematical Sciences, NJIT
Thesis: Stationary probability distributions of stochastic gradient descent and the success and failure of the diffusion approximation

Linwan Feng, Ph.D., Summer 2020
Co-advised with Wooyoung Choi
Department of Mathematical Sciences, NJIT
Thesis: Efficient time-stepping approaches for the dispersive shallow water equations

Mahdi Bandegi, Ph.D., Fall 2019
Department of Mathematical Sciences, NJIT
Thesis: Convex relaxations of a continuum aggregation model, and their efficient numerical solution

Preprints

D. Shirokoff, P. Zaleski
Convergence of Markov Chains for Constant Step-size Stochastic Gradient Descent with Separable Functions

A. Biswas, D. Ketcheson, S. Roberts, B. Seibold, D. Shirokoff
Explicit Runge Kutta Methods that Alleviate Order Reduction

Publications

A. Juhl, D. Shirokoff
Algebraic conditions for stability in Runge-Kutta methods and their certification via semidefinite programming
Applied Numerical Mathematics, 207 (2025), pp 136-155.

A. Biswas, D. Ketcheson, B. Seibold, D. Shirokoff
Algebraic structure of the weak stage order conditions for Runge-Kutta methods
SIAM Journal on Numerical Analysis, 62,1 (2024), pp. 48-72.

R. R. Rosales, B. Seibold, D. Shirokoff, D. Zhou
Spatial manifestations of order reduction in Runge-Kutta methods for initial boundary value problems
Communications in Mathematical Sciences, 22, 3, (2024), pp 613-653.

A. Biswas, D. Ketcheson, B. Seibold, D. Shirokoff
Design of DIRK schemes with high weak stage order
Communications in Applied Mathematics and Computational Science 18, 1 (2023), pp 1-28.

R. R. Rosales, B. Seibold, D. Shirokoff, D. Zhou
High-order finite element methods for a pressure Poisson equation reformulation of the Navier-Stokes equations with electric boundary conditions
Computer Methods in Applied Mechanics and Engineering, 373, 1 January (2021), 113451.

D. Ketcheson, B. Seibold, D. Shirokoff, D. Zhou
DIRK Schemes with high weak stage order
In: Sherwin S., Moxey D., Peiro J., Vincent P., Schwab C. (eds)
Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018.
Lecture Notes in Computational Science and Engineering, vol 134. Springer, Cham.

W. Batson, L. Cummings, D. Shirokoff, L. Kondic
Oscillatory thermocapillary instability of a film heated by a thick substrate
Journal of Fluid Mechanics, 872 (2019), pp 928-962.

B. Seibold, D. Shirokoff, D. Zhou
Unconditional stability for multistep ImEx schemes: Practice
Journal of Computational Physics, 376, 1, (2019), pp 295-321.

M. Bandegi, D. Shirokoff
Approximate global minimizers to pairwise interaction problems via convex relaxation
SIAM Journal on Applied and Dynamical Systems, 17, 1, (2018), pp 417-456.

R. R. Rosales, B. Seibold, D. Shirokoff, D. Zhou
Unconditional stability for multistep ImEx schemes: Theory
SIAM Journal on Numerical Analysis, 55, 5, (2017), pp 2336-2360.

R. Galagusz, D. Shirokoff, J-C. Nave
A Fourier penalty method for solving the time-dependent Maxwell's equations in domains with curved boundaries
Journal of Computational Physics, 306, 1, (2016), pp 167-198,

X. Cheng, D. Li, D. Shirokoff, B. Wetton
On the spectral gap of a square distance matrix
Journal of Statistical Physics, 166, 3-4, (2016), pp 1029-1035.

D. Shirokoff, J-C. Nave
A Sharp-interface active penalty method for the incompressible Navier-Stokes equations
Journal of Scientific Computing, 62, 1, (2015), pp 53-77.

D. Shirokoff, R. Choksi, J-C. Nave
Sufficient conditions for global minimality of metastable states in a class of non-convex functionals: a simple approach via quadratic lower bounds
Journal of Nonlinear Science, 25, 3, (2015), pp 539-582.

D. Zhou, B. Seibold, D. Shirokoff, P. Chidyagwai, R. Rosales
Meshfree finite differences for a vector Poisson and pressure Poisson equation with electric boundary conditions
Meshfree methods for Partial Differential Equations VII
Lecture Notes in Computational Science and Engineering,
Vol. 100 Griebel, M. and Schweitzer, M.A. (ed.), Springer (2014).

D. Shirokoff
Bouncing droplets on a billiard table
Chaos: An Interdisciplinary Journal of Nonlinear Science, 23, 013115 (2013).

D. Shirokoff, R. R. Rosales
An efficient method for the incompressible Navier-Stokes equations on irregular domains with no-slip boundary conditions, high order up to the boundary
Journal of Computational Physics, 230, 23, (2011), pp 8619-8646.

D. Shirokoff
Renormalized waves and thermalization of the Klein-Gordon equation
Physical Review E, 83, 046217, (2011).

M. A. Amin, D. Shirokoff
Flat-top oscillons in an expanding universe
Physical Review D, 81, 085045 (2010).

D. Shirokoff, C. H. F. Fung, H. K. Lo
Discrete rotational symmetry and quantum key distribution protocols
Physical Review A, 75, 032341 (2007).

K. Samokhin, D. Shirokoff
Phenomenological theory of superconductivity near domain walls in ferromagnets
Physical Review B, 71, 104527 (2005).

I. A pressure Poisson method for the incompressible Navier-Stokes equations : II. Long time behavior of the Klein-Gordon equations, Ph.D. Thesis, Massachusetts Institute of Technology, 2011.

Discrete rotational symmetry and quantum key distribution protocols, Undergraduate Thesis, University of Toronto, 2006.

NSF DMS-2309727
August 1, 2023 - July 31, 2026

NSF DMS-2012268
August 15, 2020 - July 31, 2023

NSF DMS-1719693
August 1, 2017 - July 31, 2020

Simons Foundation #359610
Collaboration Grant for Mathematicians
September 1, 2015 - August 31, 2017