Related papers: Hadamard integrator for time-dependent wave equati…
The Hadamard parametrix is a representation of the short-distance singularity structure of the Feynman Green's function for a quantum field on a curved space-time background. Subtracting these divergent terms regularizes the Feynman Green's…
We formulate a time-dependent Fluctuating Local Field (TD-FLF) method for correlated fermion dynamics, extending the stationary FLF approach. The wavefunction is approximated as an ensemble of non-interacting states subject to a classical…
An exponentially convergent numerical method for solving a differential equation with a right-hand fractional Riemann-Liouville time-derivative and an unbounded operator coefficient in Banach space is proposed and analysed for a…
The scattering of electromagnetic waves from obstacles with wave-material interaction in thin layers on the surface is described by generalized impedance boundary conditions, which provide effective approximate models. In particular, this…
We devise a new time-stepping algorithm for two-dimensional nonlinear unsteady surface and interfacial waves. The algorithm uses Cauchy's integral formula, which only requires information on the interface, to solve Laplace equation by using…
It is well known that the Lagrangian and Hamiltonian descriptions of field theories are equivalent at the discrete time level when variational integrators are used. Besides the symplectic Hamiltonian structure, many physical systems exhibit…
A variational formulation of accelerated optimization on normed spaces was recently introduced by considering a specific family of time-dependent Bregman Lagrangian and Hamiltonian systems whose corresponding trajectories converge to the…
In this paper we propose a novel way to integrate time-evolving partial differential equations that contain nonlinear advection and stiff linear operators, combining exponential integration techniques and semi-Lagrangian methods. The…
We investigate the applicability of the two existing versions of a time-dependent Gutzwiller approximation (TDGA) beyond the frequently used limit of infinite spatial dimensions. To this end, we study the two-particle response functions of…
A fully implicit finite difference scheme has been developed to solve the hydrodynamic equations coupled with radiation transport. Solution of the time dependent radiation transport equation is obtained using the discrete ordinates method…
We introduce a numerical method for the solution of the time-dependent Schrodinger equation with a smooth potential, based on its reformulation as a Volterra integral equation. We present versions of the method both for periodic boundary…
A novel semi-Lagrangian method is introduced to solve numerically the Euler equation for ideal incompressible flow in arbitrary space dimension. It exploits the time-analyticity of fluid particle trajectories and requires, in principle,…
We report a three-dimensional numerical implementation of multiconfiguration time-dependent Hartree-Fock (MCTDHF) based on a multi-resolution Cartesian grid, with no need to assume any symmetry of molecular structure. We successfully…
The Vlasov-Poisson system, modeling the evolution of non-collisional plasmas in the electrostatic limit, is approx- imated by a Semi-Lagrangian technique. Spectral methods of periodic type are implemented through a collocation approach.…
We have developed a time propagation scheme for the Kadanoff-Baym equations for general inhomogeneous systems. These equations describe the time evolution of the nonequilibrium Green function for interacting many-body systems in the…
In this paper we obtain a Hadamard type formula for simple eigenvalues and an analog to the Rayleigh-Faber-Krahn inequality for a class of nonlocal eigenvalue problems. Such class of equations include among others, the classical nonlocal…
In this paper, a new approach for constructing Lagrangians for driven and undriven linearly damped systems is proposed, by introducing a redefined time coordinate and an associated coordinate transformation to ensure that the resulting…
Recently, Lobb and Nijhoff initiated the study of variational (Lagrangian) structure of discrete integrable systems from the perspective of multi-dimensional consistency. In the present work, we follow this line of research and develop a…
The augmented Lagrangian (AL) method has been successfully applied for solving the full waveform inversion (FWI) problem. In AL-based FWI, the Lagrange multipliers serve as source extensions, offering several advantages to the inversion,…
The method proposed by Inomata and his collaborators allows us to transform a damped Caldiroli-Kanai oscillator with time-dependent frequency to one with constant frequency and no friction by redefining the time variable, obtained by…