Related papers: Fast integrators for dynamical systems with severa…
We propose a novel method for fast and scalable evaluation of periodic solutions of systems of ordinary differential equations for a given set of parameter values and initial conditions. The equations governing the system dynamics are…
Complex systems often show macroscopic coherent behavior due to the interactions of microscopic agents like molecules, cells, or individuals in a population with their environment. However, simulating such systems poses several…
The Boris algorithm, a closely related variational integrator and a newly proposed filtered variational integrator are studied when they are used to numerically integrate the equations of motion of a charged particle in a non-uniform strong…
We present a novel approach to investigate the long-time stochastic dynamics of multi-dimensional classical systems, in contact with a heat-bath. When the potential energy landscape is rugged, the kinetics displays a decoupling of short and…
Asymptotic homogenisation is considered for problems with integral constraints imposed on a slowly-varying microstructure; an insulator with an array of perfectly dielectric inclusions of slowly varying size serves as a paradigm. Although…
We present two types of meta-algorithm that can greatly improve the accuracy of existing algorithms for integrating the equations of motion of dynamical systems. The first meta-algorithm takes an integrator that is time-symmetric only for…
A valuable step in the modeling of multiscale dynamical systems in fields such as computational chemistry, biology, materials science and more, is the representative sampling of the phase space over long timescales of interest; this task is…
By a high-order numerical homogenization method, a heterogeneous multiscale scheme was developed in Jin & Li (2022) for evolving differential equations containing two time scales. In this paper, we further explore the technique to propose…
Time integration methods for solving initial value problems are an important component of many scientific and engineering simulations. Implicit time integrators are desirable for their stability properties, significantly relaxing…
Heterogeneous multiscale methods (HMM) combine molecular accuracy of particle-based simulations with the computational efficiency of continuum descriptions to model flow in soft matter liquids. In these schemes, molecular simulations…
Understanding the dynamics of phase boundaries in fluids requires quantitative knowledge about the microscale processes at the interface. We consider the sharp-interface motion of compressible two-component flow, and propose a heterogeneous…
Different possible sources are discussed for enhancement of the calculation time when solving ordinary differential equations systems to forecast space objects' motion. This paper presents an approach for building an integrator of ordinary…
In this paper we propose a numerical method to solve a 2D advection-diffusion equation, in the highly oscillatory regime. We use an efficient and robust integrator which leads to an accurate approximation of the solution without any time…
A single-step high-order implicit time integration scheme with controllable numerical dissipation at high frequencies is presented for the transient analysis of structural dynamic problems. The amount of numerical dissipation is controlled…
First of all, this paper presents some improvements of DSMC method in the form of new schemes and approaches, that, for a wide class of problems, increase performance and reduce the demands on computer resources. The most important…
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,…
Many biological and physical systems exhibit behaviour at multiple spatial, temporal or population scales. Multiscale processes provide challenges when they are to be simulated using numerical techniques. While coarser methods such as…
We propose an efficient approach for time integration of Klein-Gordon equations with highly oscillatory in time input terms. The new methods are highly accurate in the entire range, from slowly varying up to highly oscillatory regimes. Our…
Spatially and temporally varying coefficient (STVC) models are currently attracting attention as a flexible tool to explore the spatio-temporal patterns in regression coefficients. However, these models often struggle with balancing…
In recent decades, there have been many attempts to construct symplectic integrators with variable time steps, with rather disappointing results. In this paper we identify the causes for this lack of performance, and find that they fall…