Related papers: Reversible time-step adaptation for the integratio…
Stiff hyperbolic balance laws exhibit large spectral gaps, especially if the relaxation term significantly varies in space. Using examples from rarefied gases and the general form of the underlying balance law model, we perform a detailed…
The large dynamic range in some astrophysical N-body problems led to the use of adaptive multi-time-steps; however, the search for optimal strategies is still challenging. We numerically quantify the performance of the hierarchical…
We introduce a new strategy for coupling the parallel in time (parareal) iterative methodology with multiscale integrators. Following the parareal framework, the algorithm computes a low-cost approximation of all slow variables in the…
We present a new method for developing time step controllers based on a technique from the field of machine learning. This method is applicable to stable time integrators that have an embedded scheme, i.e., that have local error estimation…
The thermodynamic behaviour of self-gravitating $N$-body systems has been worked out by borrowing a standard method from Molecular Dynamics: the time averages of suitable quantities are numerically computed along the dynamical trajectories…
Center-based models are used to simulate the mechanical behavior of biological cells during embryonic development or cancer growth. To allow for the simulation of biological populations potentially growing from a few individual cells to…
We introduce an explicit, adaptive time-stepping scheme for the simulation of SPDEs with one-sided Lipschitz drift coefficients. Strong convergence rates are proven for the full space-time discretisation with multiplicative trace-class…
The automatic selection of an appropriate time step size has been considered extensively in the literature. However, most of the strategies developed operate under the assumption that the computational cost (per time step) is independent of…
The reduction of the computational effort is desirable for the simulation of marine ecosystem models. Using a marine ecosystem model, the assessment and the validation of annual periodic solutions (i.e., steady annual cycles) against…
In this paper, we investigate the use of higher-order exponential Rosenbrock time integration methods on the shallow water equations on the sphere. This stiff, nonlinear model provides a testing ground for accurate and stable time…
In this paper, we present a new hybrid algorithm for the time integration of collisional N-body systems. In this algorithm, gravitational force between two particles is divided into short-range and long-range terms, using a…
This study assesses the relative importance of time integration error in present-day climate simulations conducted with the atmosphere component of the Energy Exascale Earth System Model version 1 (EAMv1) at 1-degree horizontal resolution.…
Adaptivity and local mesh refinement are crucial for the efficient numerical simulation of wave phenomena in complex geometry. Local mesh refinement, however, can impose a tiny time-step across the entire computational domain when using…
Molecular dynamics is one of the most commonly used approaches for studying the dynamics and statistical distributions of many physical, chemical, and biological systems using atomistic or coarse-grained models. It is often the case,…
Platform trials can evaluate the efficacy of several treatments compared to a control. The number of treatments is not fixed, as arms may be added or removed as the trial progresses. Platform trials are more efficient than independent…
Cosmological simulations require the use of a multiple time-stepping scheme. Without such a scheme, cosmological simulations would be impossible due to their high level of dynamic range; over eleven orders of magnitude in density. Such a…
This letter proposes a predictor-corrector method to strike a balance between simulation accuracy and efficiency by appropriately tuning the numerical integration step length of a power system time-domain simulation. Numerical tests…
In this note we approach the classical, Newtonian, gravitational $N$-body problem by mean of a new, original numerical integration method. After a short summary of the fundamental characteristics of the problem, including a sketch of some…
In the context of state-space models, skeleton-based smoothing algorithms rely on a backward sampling step which by default has a $\mathcal O(N^2)$ complexity (where $N$ is the number of particles). Existing improvements in the literature…
Many recently introduced enhanced sampling techniques are based on biasing coarse descriptors (collective variables) of a molecular system on the fly. Sometimes the calculation of such collective variables is expensive and becomes a…