13 citations · 30 across the 15 of their papers we have counts for
15 papers
Explicit invariant-preserving integration of differential equations using homogeneous projection
Benjamin Kwanen Tapley
We develop a general framework for numerically solving differential equations while preserving invariants. As in standard projection methods, we project an arbitrary base integrato…
Learning mechanical systems from real-world data using discrete forced Lagrangian dynamics
Martine Dyring Hansen, Elena Celledoni, Benjamin Kwanen Tapley
We introduce a data-driven method for learning the equations of motion of mechanical systems directly from position measurements, without requiring access to velocity data. This is…
Symplectic Neural Networks Based on Dynamical Systems
Benjamin K Tapley
We present and analyze a framework for designing symplectic neural networks (SympNets) based on geometric integrators for Hamiltonian differential equations. The SympNets are unive…
Linear Darboux polynomials for Lotka-Volterra systems, trees and superintegrable families
G. R. W. Quispel, Benjamin K. Tapley, D. I. McLaren +1
We present a method to construct superintegrable -component Lotka-Volterra systems with parameters. We apply the method to Lotka-Volterra systems with components for…
Coalgebra symmetry for discrete systems
G. Gubbiotti, D. Latini, B. K. Tapley
In this paper we introduce the notion of coalgebra symmetry for discrete systems. With this concept we prove that all discrete radially symmetric systems in standard form are quasi…
Geometric integration of ODEs using multiple quadratic auxiliary variables
Benjamin K Tapley
We present a novel numerical method for solving ODEs while preserving polynomial first integrals. The method is based on introducing multiple quadratic auxiliary variables to refor…
On the preservation of second integrals by Runge-Kutta methods
Benjamin K Tapley
One can elucidate integrability properties of ordinary differential equations (ODEs) by knowing the existence of second integrals (also known as weak integrals or Darboux polynomia…
An integral model based on slender body theory, with applications to curved rigid fibers
Helge I. Andersson, Elena Celledoni, Laurel Ohm +2
We propose a novel integral model describing the motion of curved slender fibers in viscous flow, and develop a numerical method for simulating dynamics of rigid fibers. The model…
Computational geometric methods for preferential clustering of particle suspensions
Benjamin K. Tapley, Helge I. Andersson, Elena Celledoni +1
A geometric numerical method for simulating suspensions of spherical and non-spherical particles with Stokes drag is proposed. The method combines divergence-free matrix-valued rad…
A slender body model for thin rigid fibers: validation and comparisons
Laurel Ohm, Benjamin K. Tapley, Helge I. Andersson +2
In this paper we consider a computational model for the motion of thin, rigid fibers in viscous flows based on slender body theory. Slender body theory approximates the fluid veloc…
Using discrete Darboux polynomials to detect and determine preserved measures and integrals of rational maps
E Celledoni, C Evripidou, D I McLaren +4
In this Letter we propose a systematic approach for detecting and calculating preserved measures and integrals of a rational map. The approach is based on the use of cofactors and…
Detecting and determining preserved measures and integrals of birational maps
Elena Celledoni, Charalambos Evripidou, David McLaren +3
In this paper we use the method of discrete Darboux polynomials to calculate preserved measures and integrals of rational maps. The approach is based on the use of cofactors and Da…
Computing cost-effective particle trajectories in numerically calculated incompressible fluids using geometric methods
Benjamin K Tapley
We present an novel algorithm for tracking massless solid particles in a divergence-free velocity field that is only available at discrete points in space and time such as those ar…
Symplectic integration of PDEs using Clebsch variables
Robert I McLachlan, Christian Offen, Benjamin K Tapley
Many PDEs (Burgers' equation, KdV, Camassa-Holm, Euler's fluid equations,...) can be formulated as infinite-dimensional Lie-Poisson systems. These are Hamiltonian systems on manifo…
A novel approach to rigid spheroid models in viscous flows using operator splitting methods
Benjamin Tapley, Elena Celledoni, Brynjulf Owren +1
Calculating cost-effective solutions to particle dynamics in viscous flows is an important problem in many areas of industry and nature. We implement a second-order symmetric split…