相关论文: Hadamard integrator for time-dependent wave equati…

As a phase space language for quantum mechanics, the Wigner function approach bears a close analogy to classical mechanics and has been drawing growing attention, especially in simulating quantum many-body systems. However, deterministic…

This paper proposes a frequency-time hybrid solver for the time-dependent wave equation in two-dimensional interior spatial domains. The approach relies on four main elements, namely, 1) A multiple scattering strategy that decomposes a…

A challenge in modeling time-dependent strong-field processes such as high-harmonic generation for many-body systems, is how to effectively represent the electronic continuum. We apply Rothe's method to the time-dependent Hartree-Fock…

Time-harmonic solutions to the wave equation can be computed in the frequency or in the time domain. In the frequency domain, one solves a discretized Helmholtz equation, while in the time domain, the periodic solutions to a discretized…

In this paper, we aim to develop a hybridizable discontinuous Galerkin (HDG) method for the indefinite time-harmonic Maxwell equations with the perfectly conducting boundary in the three-dimensional space. First, we derive the wavenumber…

Magneto-hydrodynamics is one of the foremost models in plasma physics with applications in inertial confinement fusion, astrophysics and elsewhere. Advanced numerical methods are needed to get an insight into the complex physical phenomena.…

Modeling time-harmonic Maxwell problems in heterogeneous media presents significant mathematical and computational challenges. Due to the inherent non-elliptic structure and non-coercive nature of Maxwell equations, conventional methods…

The guiding-center reduction is studied using gyro-gauge-independent coordinates. The Lagrangian 1-form of charged particle dynamics is Lie transformed without introducing a gyro-gauge, but using directly the unit vector of the component of…

In this paper we introduce a model of relativistic short wave-long wave interaction where the short waves are described by the massless $1+3$-dimensional Thirring model of nonlinear Dirac equation and the long waves are described by the…

Efficient and accurate numerical propagation of the time dependent Schroedinger equation is a problem with applications across a wide range of physics. This paper develops an efficient, trivially parallelizeable method for relaxing a trial…

In this work, we introduce a new realization of exactly-solvable time-dependent Hamiltonians based on the solutions of the fourth Painlev\'e and the Ermakov equations. The latter is achieved by introducing a shape-invariant condition…

This work considers a short-term, continuous time setting characterized by a coupled power supply system controlled exclusively by a single provider and comprising a cascade of hydropower systems (dams), fossil fuel power stations, and a…

In this paper, we determine the wave front set of solutions to the Schr\"{o}dinger equation with time-dependent magnetic fields. We considered time-dependent and `not so small' magnetic fields through the method using the wave packet…

We add a time-dependent potential to the inhomogeneous wave equation and consider the task of reconstructing this potential from measurements of the wave field. This dynamic inverse problem becomes more involved compared to static…

Time-dependent quantum mechanics provides an intuitive picture of particle propagation in external fields. Semiclassical methods link the classical trajectories of particles with their quantum mechanical propagation. Many analytical results…

To solve the Cahn-Hilliard equation numerically, a new time integration algorithm is proposed, which is based on a combination of the Eyre splitting and the local iteration modified (LIM) scheme. The latter is employed to tackle the…

In this paper we extend analysis of the WaveHoltz iteration -- a time-domain iterative method for the solution of the Helmholtz equation. We expand the previous analysis of energy conserving problems and prove convergence of the WaveHoltz…

The reductive perturbation method has been employed to derive the Korteweg-de Vries (KdV) equation for small but finite amplitude electrostatic waves. The Lagrangian of the time fractional KdV equation is used in similar form to the…

A new Hamiltonian formulation for the fully nonlinear water-wave problem over variable bathymetry is derived, using an exact, vertical series expansion of the velocity potential, in conjunction with Luke's variational principle. The…

We build an efficient and unitary (hence stable) method for the solution of the semi-classical Schr\"odinger equation subject with explicitly time-dependent potentials. The method is based on a combination of the Zassenhaus decomposition…