134 citations · 337 across the 20 of their papers we have counts for
21 papers
Adaptive Diagonally Implicit Runge-Kutta Methods Devoid of Order Reduction for Semilinear ODEs
Steven B. Roberts, Abhijit Biswas, David Shirokoff +1
Diagonally implicit Runge-Kutta (DIRK) methods are a prominent class of numerical methods for solving stiff systems of ordinary differential equations (ODEs). Stiffness does not on…
A Stiff Order Condition Theory for Runge-Kutta Methods Applied to Semilinear ODEs
Steven B. Roberts, David Shirokoff, Abhijit Biswas +1
Classical convergence theory of Runge-Kutta methods assumes that the time step is small relative to the Lipschitz constant of the ordinary differential equation (ODE). For stiff pr…
Convergence of Markov Chains for Constant Step-size Stochastic Gradient Descent with Separable Functions
David Shirokoff, Philip Zaleski
Stochastic gradient descent (SGD) is a popular algorithm for minimizing objective functions that arise in machine learning. For constant step-sized SGD, the iterates form a Markov…
Algebraic Conditions for Stability in Runge-Kutta Methods and Their Certification via Semidefinite Programming
Austin Juhl, David Shirokoff
In this work, we present approaches to rigorously certify - and -stability in Runge-Kutta methods through the solution of convex feasibility problems defined by linear mat…
Explicit Runge Kutta Methods that Alleviate Order Reduction
Abhijit Biswas, David I. Ketcheson, Steven Roberts +2
Explicit Runge--Kutta (RK) methods are susceptible to a reduction in the observed order of convergence when applied to initial-boundary value problem with time-dependent boundary c…
Design of DIRK Schemes with High Weak Stage Order
Abhijit Biswas, David Ketcheson, Benjamin Seibold +1
Runge-Kutta (RK) methods may exhibit order reduction when applied to certain stiff problems. While fully implicit RK schemes exist that avoid order reduction via high-stage order,…
Algebraic Structure of the Weak Stage Order Conditions for Runge-Kutta Methods
Abhijit Biswas, David Ketcheson, Benjamin Seibold +1
Runge-Kutta (RK) methods may exhibit order reduction when applied to stiff problems. For linear problems with time-independent operators, order reduction can be avoided if the meth…
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 +1
Pressure Poisson equation (PPE) reformulations of the incompressible Navier-Stokes equations (NSE) replace the incompressibility constraint by a Poisson equation for the pressure a…
DIRK Schemes with High Weak Stage Order
David Ketcheson, Benjamin Seibold, David Shirokoff +1
Runge-Kutta time-stepping methods in general suffer from order reduction: the observed order of convergence may be less than the formal order when applied to certain stiff problems…
Unconditional Stability for Multistep ImEx Schemes: Practice
Benjamin Seibold, David Shirokoff, Dong Zhou
This paper focuses on the question of how unconditional stability can be achieved via multistep ImEx schemes, in practice problems where both the implicit and explicit terms are al…
Spatial Manifestations of Order Reduction in Runge-Kutta Methods for Initial Boundary Value Problems
Rodolfo Ruben Rosales, Benjamin Seibold, David Shirokoff +1
This paper studies the spatial manifestations of order reduction that occur when time-stepping initial-boundary-value problems (IBVPs) with high-order Runge-Kutta methods. For such…
Unconditional Stability for Multistep ImEx Schemes: Theory
Rodolfo Ruben Rosales, Benjamin Seibold, David Shirokoff +1
This paper presents a new class of high order linear ImEx multistep schemes with large regions of unconditional stability. Unconditional stability is a desirable property of a time…
Approximate global minimizers to pairwise interaction problems via convex relaxation
Mahdi Bandegi, David Shirokoff
We present a new approach for computing approximate global minimizers to a large class of non-local pairwise interaction problems defined over probability distributions. The approa…
A Fourier penalty method for solving the time-dependent Maxwell's equations in domains with curved boundaries
Ryan Galagusz, David Shirokoff, Jean-Christophe Nave
We present a high order, Fourier penalty method for the Maxwell's equations in the vicinity of perfect electric conductor boundary conditions. The approach relies on extending the…
Meshfree finite differences for vector Poisson and pressure Poisson equations with electric boundary conditions
Dong Zhou, Benjamin Seibold, David Shirokoff +2
We demonstrate how meshfree finite difference methods can be applied to solve vector Poisson problems with electric boundary conditions. In these, the tangential velocity and the i…
A Sharp-Interface Active Penalty Method for the Incompressible Navier-Stokes Equations
David Shirokoff, Jean-Christophe Nave
The volume penalty method provides a simple, efficient approach for solving the incompressible Navier-Stokes equations in domains with boundaries or in the presence of moving objec…
Bouncing droplets on a billiard table
David Shirokoff
In a set of experiments, Couder et. al. demonstrate that an oscillating fluid bed may propagate a bouncing droplet through the guidance of the surface waves. We present a dynamical…
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
Common efficient schemes for the incompressible Navier-Stokes equations, such as projection or fractional step methods, have limited temporal accuracy as a result of matrix splitti…
Flat-top oscillons in an expanding universe
Mustafa A. Amin, David Shirokoff
Oscillons are extremely long lived, oscillatory, spatially localized field configurations that arise from generic initial conditions in a large number of non-linear field theories.…
Discrete Rotational Symmetry and Quantum Key Distribution Protocols
David Shirokoff, Chi-Hang Fred Fung, Hoi-Kwong Lo
We study the role of discrete rotational symmetry in quantum key distribution by generalizing the well-known Bennett-Brassard 1984 (BB84) and Scarani-Acin-Ribordy-Gisin 2004 (SARG0…
Phenomenological theory of superconductivity near domain walls in ferromagnets
K. V. Samokhin, D. Shirokoff
We develop a phenomenological model of superconductivity near a domain wall in a ferromagnet. In addition to the electromagnetic interaction of the order parameter with the ferroma…