Related papers: Time exponential integrator Fourier pseudospectral…
A group of high order Gautschi-type exponential wave integrators (EWIs) Fourier pseudospectral method are proposed and analyzed for solving the nonlinear Klein-Gordon equation (KGE) in the nonrelativistic limit regime, where a parameter…
In this paper, we formulate and analyse exponential integrations when applied to nonlinear Schr\"{o}dinger equations in a normal or highly oscillatory regime. A kind of exponential integrators with energy preservation, optimal convergence…
With the advent of PW class lasers, the very large laser intensities attainable on-target should enable the production of intense high order Doppler harmonics from relativistic laser-plasma mirrors interactions. At present, the modeling of…
In this paper, in order to improve the spatial accuracy, the exponential integrator Fourier Galerkin method (EIFG) is proposed for solving semilinear parabolic equations in rectangular domains. In this proposed method, the spatial…
A time domain electric field volume integral equation (TD-EFVIE) solver is proposed for analyzing electromagnetic scattering from dielectric objects with Kerr nonlinearity. The nonlinear constitutive relation that relates electric flux and…
We prove Strichartz estimates for Maxwell equations in media in the fully anisotropic case with H\"older-continuous coefficients. To this end, we use the FBI transform to conjugate the problem to phase space. After reducing to a scalar…
We consider the numerical discretization of the time-domain Maxwell's equations with an energy-conserving discontinuous Galerkin finite element formulation. This particular formulation allows for higher order approximations of the electric…
A novel efficient and high accuracy numerical method for the time-fractional differential equations (TFDEs) is proposed in this work. We show the equivalence between TFDEs and the integer-order extended parametric differential equations…
This paper develops a strong computational approach to simulate a three-dimensional nonlinear radiation-conduction model in optically thick media, subject to suitable initial and boundary conditions. The space derivatives are approximated…
Numerical schemes for the solution of the Euler equations have recently been developed, which involve the discretisation of the internal energy equation, with corrective terms to ensure the correct capture of shocks, and, more generally,…
We consider the numerical integration of the Gross-Pitaevskii equation with a potential trap given by a time-dependent harmonic potential or a small perturbation thereof. Splitting methods are frequently used with Fourier techniques since…
A new algorithm for the stable solution of a three-dimensional scalar inverse problem of acoustic sounding of an inhomogeneous medium in a cylindrical region is proposed. The data of the problem is the complex amplitude of the wave field,…
The goal of this work is to study the electromagnetic scattering problem of time-domain Maxwell's equations in an unbounded structure. An exact transparent boundary condition is developed to reformulate the scattering problem into an…
Numerical simulation of wave propagation in an infinite medium is made possible by surrounding a finite region by a perfectly matched layer (PML). Using this approach a generalized three-dimensional (3D) formulation is proposed for…
An FFT-based algorithm is developed to simulate the propagation of elastic waves in heterogeneous $d$-dimensional rectangular shape domains. The method allows one to prescribe the displacement as a function of time in a subregion of the…
We present a spectrally accurate fast algorithm for evaluating the solution to the scalar wave equation in free space driven by a large collection of point sources in a bounded domain. With $M$ sources temporally discretized by $N_t$ time…
This paper discusses a fast direct solver using boundary integral equations for Helmholtz transmission problems involving multiple inclusions in two dimensions. Efficiently addressing scattering problems in the presence of numerous…
The advection-diffusion and wave equations are the fundamental equations governing any physical law and therefore arise in many areas of physics and astrophysics. For complex problems and geometries, only numerical simulations can give…
Seismic imaging is a major challenge in geophysics with broad applications. It involves solving wave propagation equations with absorbing boundary conditions (ABC) multiple times. This drives the need for accurate and efficient numerical…
Due to the nonlocal feature of fractional differential operators, the numerical solution to fractional partial differential equations usually requires expensive memory and computation costs. This paper develops a fast scheme for fractional…