Related papers: A New Scheme for Solving High-Order DG Discretizat…
Radiation is crucial not only for observing astrophysical objects, but also for transporting energy and momentum. However, accurate on-the-fly radiation transport in astrophysical simulations is challenging and computationally expensive.…
This article presents a high order conservative flux optimization (CFO) finite element method for the elliptic diffusion equations. The numerical scheme is based on the classical Galerkin finite element method enhanced by a flux…
We develop an asymptotic preserving scheme for the gray radiative transfer equation. Two asymptotic regimes are considered: one is a diffusive regime described by a nonlinear diffusion equation for the material temperature; the other is a…
This paper is devoted to a discussion of the Discrete Fourier Transform (DFT) representation of a chaotic finite-duration sequence. This representation has the advantage that is itself a finite-duration sequence corresponding to samples…
In this work, we tackle the resolution of partial differential equations (PDEs) on digital quantum computers. Two fundamental PDEs are addressed: the anisotropic diffusion equation and the anisotropic convection equation. We present a…
One critical challenge in 6D object pose estimation from a single RGBD image is efficient integration of two different modalities, i.e., color and depth. In this work, we tackle this problem by a novel Deep Fusion Transformer~(DFTr) block…
In this paper, we propose and analyze a new semi-implicit stochastic multiscale method for the radiative heat transfer problem with additive noise fluctuation in composite materials. In the proposed method, the strong nonlinearity term…
The nonlinear Fourier transform (NFT), a powerful tool in soliton theory and exactly solvable models, is a method for solving integrable partial differential equations governing wave propagation in certain nonlinear media. The NFT…
We present a new direct logarithmically optimal in theory and fast in practice algorithm to implement the high order finite element method on multi-dimensional rectangular parallelepipeds for solving PDEs of the Poisson kind. The key points…
We have developed an algorithm for transferring radiation in three-dimensional space. The algorithm computes radiation source and sink terms using the Fast Fourier Transform (FFT) method, based on a formulation in which the integral of any…
Trefftz schemes are high-order Galerkin methods whose discrete spaces are made of elementwise exact solutions of the underlying PDE. Trefftz basis functions can be easily computed for many PDEs that are linear, homogeneous, and have…
The radiative transfer equation (RTE) is a cornerstone for describing the propagation of electromagnetic radiation in a medium, with applications spanning atmospheric science, astrophysics, remote sensing, and biomedical optics. Despite its…
In this paper, we propose a novel neural network approach, termed DeepRTE, to address the steady-state Radiative Transfer Equation (RTE). The RTE is a differential-integral equation that governs the propagation of radiation through a…
Pseudo-spectral method is one of the most accurate techniques for simulating turbulent flows. Fast Fourier transform (FFT) is an integral part of this method. In this paper, we present a new procedure to compute FFT in which we save…
An approximate method based on adiabatic time dependent density functional theory (TDDFT) is presented, that allows for the description of the electron dynamics in nanoscale junctions under arbitrary time dependent external potentials. In…
We present a scattering approach for the study of the transport and thermodynamics of quantum systems strongly coupled to their thermal environment(s). This formalism recovers the standard non-equilibrium Green's function expressions for…
In this work, we consider the numerical solution of an initial boundary value problem for the distributed order time fractional diffusion equation. The model arises in the mathematical modeling of ultra-slow diffusion processes observed in…
We propose a hybrid spatial discretization for the radiative transport equation that combines a second-order discontinuous Galerkin (DG) method and a second-order finite volume (FV) method. The strategy relies on a simple operator splitting…
This paper proposes a new numerical method based on the Chebyshev wavelets (CWs) to solve the variable-order time fractional mobile-immobile advection-dispersion equation. To do this, a new operational matrix of variable-order fractional…
In this paper, a new family of implicit compact finite difference schemes for computation of unsteady convection-diffusion equation with variable convection coefficient is proposed. The schemes are fourth order accurate in space and second…