相关论文: Variable time-stepping exponential integrators for…

This article deals with the numerical integration in time of nonlinear Schr\"odinger equations. The main application is the numerical simulation of rotating Bose-Einstein condensates. The authors perform a change of unknown so that the…

An efficient, iterative semi-implicit (SI) numerical method for the time integration of stiff wave systems is presented. Physics-based assumptions are used to derive a convergent iterative formulation of the SI scheme which enables the…

The time dependent non-equilibrium radiation diffusion equations are important for solving the transport of energy through radiation in optically thick regimes and find applications in several fields including astrophysics and inertial…

Conservative symmetric second-order one-step integrators are derived using the Discrete Multiplier Method for a family of vortex-blob models approximating the incompressible Euler's equations on the plane. Conservative properties and second…

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…

We present in this paper algorithms for solving stiff PDEs on the unit sphere with spectral accuracy in space and fourth-order accuracy in time. These are based on a variant of the double Fourier sphere method in coefficient space with…

Immersed boundary methods simplify mesh generation by embedding the domain of interest into an extended domain that is easy to mesh, introducing the challenge of dealing with cells that intersect the domain boundary. Combined with explicit…

It is well known that symplectic integrators lose their near energy preservation properties when variable step sizes are used. The most common approach to combine adaptive step sizes and symplectic integrators involves the Poincar\'e…

A quantitative definition of numerical stiffness for initial value problems is proposed. Exponential integrators can effectively integrate linearly stiff systems, but they become expensive when the linear coefficient is a matrix, especially…

This paper presents a new algorithm KIOPS for computing linear combinations of $\varphi$-functions that appear in exponential integrators. This algorithm is suitable for large-scale problems in computational physics where little or no…

This paper proposes several explicit and implicit multistep frequency response optimized integrators considering first or second order derivative. A prediction-based method aiming at accelerating a novel power system transient simulation…

The Empirical Valence Bond (EVB) method offers a suitable framework to obtain reactive potentials through the coupling of non-reactive force fields. However, most of the implemented functional forms for the coupling terms depend on complex…

We propose and explore a new, general-purpose method for the implicit time integration of elastica. Key to our approach is the use of a mixed variational principle. In turn its finite element discretization leads to an efficient alternating…

The objective of this work is the introduction and investigation of favourable time integration methods for the Gross--Pitaevskii equation with rotation term. Employing a reformulation in rotating Lagrangian coordinates, the equation takes…

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…

Instrumental variable methods are often used for parameter estimation in the presence of confounding. They can also be applied in stochastic processes. Instrumental variable analysis exploits moment equations to obtain estimators for causal…

The development and implementation of increasingly accurate methods for electronic structure calculations mean that, for many atomistic simulation problems, treating light nuclei as classical particles is now one of the most serious…

Molecular Dynamics method is based on solution of Newtonian differential equations of motion. A new very accurate and efficient time-reversible explicit integrator was derived on the basis of second order Tailor expansion of force. There is…

In this paper, we present a novel spectral renormalization exponential integrator method for solving gradient flow problems. Our method is specifically designed to simultaneously satisfy discrete analogues of the energy dissipation laws and…

In this paper, we analyze and provide numerical illustrations for a moving finite element method applied to convection-dominated, time-dependent partial differential equations. We follow a method of lines approach and utilize an underlying…