Related papers: Tuning symplectic integrators is easy and worthwhi…
A symplectic, symmetric, second-order scheme is constructed for particle evolution in a time-dependent field with a fixed spatial step. The scheme is implemented in one space dimension and tested, showing excellent adequacy to experiment…
In this paper, we extend several time reversible numerical integrators to solve the Lorentz force equations from second order accuracy to higher order accuracy for relativistic charged particle tracking in electromagnetic fields. A fourth…
Simulation is an efficient tool in the design and control of power electronic systems. However, quick and accurate simulation of them is still challenging, especially when the system contains a large number of switches and state variables.…
The shearing sheet is a model dynamical system that is used to study the small-scale dynamics of astrophysical disks. Numerical simulations of particle trajectories in the shearing sheet usually employ the leapfrog integrator, but this…
Two families of symplectic methods specially designed for second-order time-dependent linear systems are presented. Both are obtained from the Magnus expansion of the corresponding first-order equation, but otherwise they differ in…
Register allocation (mapping variables to processor registers or memory) and instruction scheduling (reordering instructions to increase instruction-level parallelism) are essential tasks for generating efficient assembly code in a…
Integration-by-parts reductions play a central role in perturbative QFT calculations. They allow the set of Feynman integrals contributing to a given observable to be reduced to a small set of basis integrals, and they moreover facilitate…
Symplectic integrators are widely used for long-term integration of conservative astrophysical problems due to their ability to preserve the constants of motion; however, they cannot in general be applied in the presence of nonconservative…
Reductions combine collections of input values with an associative and often commutative operator to produce collections of results. When the same input value contributes to multiple outputs, there is an opportunity to reuse partial…
The division operation is important for many areas of data processing. Especially considering today's demand for hardware accelerators for machine learning algorithms, there is a high demand for an efficient calculation of the division…
Viewing optimization methods as numerical integrators for ordinary differential equations (ODEs) provides a thought-provoking modern framework for studying accelerated first-order optimizers. In this literature, acceleration is often…
Splitting methods for the numerical integration of differential equations of order greater than two involve necessarily negative coefficients. This order barrier can be overcome by considering complex coefficients with positive real part.…
We study the efficiency of algorithms simulating a system evolving with Hamiltonian $H=\sum_{j=1}^m H_j$. We consider high order splitting methods that play a key role in quantum Hamiltonian simulation. We obtain upper bounds on the number…
Probabilistic solvers provide a flexible and efficient framework for simulation, uncertainty quantification, and inference in dynamical systems. However, like standard solvers, they suffer performance penalties for certain stiff systems,…
This article considers non-relativistic charged particle dynamics in both static and non-static electromagnetic fields, which are governed by nonseparable, possibly time-dependent Hamiltonians. For the first time, explicit symplectic…
A self-organizing particle swarm is presented. It works in dissipative state by employing the small inertia weight, according to experimental analysis on a simplified model, which with fast convergence. Then by recognizing and replacing…
This article considers Hamiltonian mechanical systems with potential functions admitting jump discontinuities. The focus is on accurate and efficient numerical approximations of their solutions, which will be defined via the laws of…
Inspired by applications in optimal control of semilinear elliptic partial differential equations and physics-integrated imaging, differential equation constrained optimization problems with constituents that are only accessible through…
Generalized Additive Runge-Kutta schemes have shown to be a suitable tool for solving ordinary differential equations with additively partitioned right-hand sides. This work develops symplectic GARK schemes for additively partitioned…
We have proposed new algorithms for the numerical integration of the equations of motion for classical spin systems. In close analogy to symplectic integrators for Hamiltonian equations of motion used in Molecular Dynamics these algorithms…