Related papers: Splitting methods for Levitron Problems
Dependable numerical results from long-time simulations require stable numerical integration schemes. For Hamiltonian systems, this is achieved with symplectic integrators, which conserve the symplectic condition and exactly solve for the…
We study numerical methods for dissipative particle dynamics (DPD), which is a system of stochastic differential equations and a popular stochastic momentum-conserving thermostat for simulating complex hydrodynamic behavior at mesoscales.…
We propose to introduce additional control in levitated optomechanics by trapping a meta-atom, i.e. a subwavelength and high-permittivity dielectric particle supporting Mie resonances. In particular, we theoretically demonstrate that…
This paper presents enhancement strategies for the Hermitian and skew-Hermitian splitting method based on gradient iterations. The spectral properties are exploited for the parameter estimation, often resulting in a better convergence. In…
A rigid body model for the dynamics of a marine vessel, used in simulations of offshore pipe-lay operations, gives rise to a set of ordinary differential equations with controls. The system is input-output passive. We propose…
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 splitting method on the governing equations for a rigid…
In this work, the benefits of the phase fitting technique are embedded in high order discrete Lagrangian integrators. The proposed methodology creates integrators with zero phase lag in a test Lagrangian in a similar way used in phase…
This paper presents an iterative method suitable for inverting semilinear problems which are important kernels in many numerical applications. The primary idea is to employ a parametrization that is able to reduce semilinear problems into…
The equations of motion of a single particle subject to an arbitrary electric and a static magnetic field form a Poisson system. We present a second-order time integration method which preserves well the Poisson structure and compare it to…
Operator splitting methods tailored to coupled linear port-Hamiltonian systems are developed. We present algorithms that are able to exploit scalar coupling, as well as multirate potential of these coupled systems. The obtained algorithms…
Symplectic integrators offer many advantages for the numerical solution of Hamiltonian differential equations, including bounded energy error and the preservation of invariant sets. Two of the central Hamiltonian systems encountered in…
A revised version of the quaternion approach for numerical integration of the equations of motion for rigid polyatomic molecules is proposed. The modified approach is based on a formulation of the quaternion dynamics with constraints. This…
We investigate the performance of various methods of symplectic integration, which are based on two part splitting of the integration operator, for the numerical integration of multidimensional Hamiltonian systems. We implement these…
Current algorithms for large-scale industrial optimization problems typically face a trade-off: they either require exponential time to reach optimal solutions, or employ problem-specific heuristics. To overcome these limitations, we…
In this paper, we provide different splitting methods for solving distributionally robust optimization problems in cases where the uncertainties are described by discrete distributions. The first method involves computing the proximity…
We consider the numerical integration of non-autonomous separable parabolic equations using high order splitting methods with complex coefficients (methods with real coefficients of order greater than two necessarily have negative…
In order to perform numerical studies of long-term stability in nonlinear Hamiltonian systems, one needs a numerical integration algorithm which is symplectic. Further, this algorithm should be fast and accurate. In this paper, we propose…
In this paper we study the split minimization problem that consists of two constrained minimization problems in two separate spaces that are connected via a linear operator that maps one space into the other. To handle the data of such a…
The goal of the present work is to solve a linear dispersive equation with variable coefficient advection on an unbounded domain. In this setting, transparent boundary conditions are vital to allow waves to leave (or even re-enter) the,…
We present several methods, which utilize symplectic integration techniques based on two and three part operator splitting, for numerically solving the equations of motion of the disordered, discrete nonlinear Schr\"odinger (DDNLS)…