相关论文: Ray Effect Mitigation for the Discrete Ordinates M…

A discrete spherical harmonics method is developed for the radiative transfer problem in inhomogeneous polarized planar atmosphere illuminated at the top by a collimated sunlight while the bottom reflects the radiation. The method expands…

Semi-discrete optimal transport (SOT), which maps a continuous probability measure to a discrete one, is a fundamental problem with wide-ranging applications. Entropic regularization is often employed to solve the SOT problem, leading to a…

Rendering highly scattering participating media using brute force path tracing is a challenge. The diffusion approximation reduces the problem to solving a simple linear partial differential equation. Flux-limited diffusion introduces…

In this paper, an improved numerical solver to evaluate the time-dependent radiative transfer equation (RTE) for underwater optical wireless communications (UOWC) is investigated. The RTE evaluates the optical path-loss of light wave in an…

Ray effect usually appears in the radiative transfer when using discrete ordinates method (DOM) in the simulations. The cause and remedy for the ray effect have been intensively investigated in the radiation community. For rarefied gas…

We develop fast and scalable methods for computing reduced-order nonlinear solutions (RONS). RONS was recently proposed as a framework for reduced-order modeling of time-dependent partial differential equations (PDEs), where the modes…

We introduce and test a new and highly efficient method for treating the thermal and radiative effects influencing the energy equation in SPH simulations of star formation. The method uses the density, temperature and gravitational…

When solving the time-dependent radiative transport equation (RTE), implicit time discretization is often employed for its robustness and stability. This results in a sequence of steady-state RTEs with identical cross-sections but varying…

This paper is concerned with a numerical solution to the scattering of a time-harmonic electromagnetic wave by a bounded and impenetrable obstacle in three dimensions. The electromagnetic wave propagation is modeled by a boundary value…

The small perturbations method has been extensively used for waves scattering by rough surfaces. The standard method developped by Rice is difficult to apply when we consider second and third order of scattered fields as a function of the…

We study an inverse scattering problem for a generic hyperbolic system of equations with an unknown coefficient called the reflectivity. The solution of the system models waves (sound, electromagnetic or elastic), and the reflectivity…

Scattering resonances have important applications in many areas of science and engineering. They are the replacement of discrete spectral data for problems on non-compact domains. In this paper, we consider the computation of scattering…

This work proposes novel techniques for the efficient numerical simulation of parameterized, unsteady partial differential equations. Projection-based reduced order models (ROMs) such as the reduced basis method employ a (Petrov-)Galerkin…

We propose a novel rolling shutter bundle adjustment method for neural radiance fields (NeRF), which utilizes the unordered rolling shutter (RS) images to obtain the implicit 3D representation. Existing NeRF methods suffer from low-quality…

Nonlinear parametric inverse problems appear in many applications and are typically very expensive to solve, especially if they involve many measurements. These problems pose huge computational challenges as evaluating the objective…

A numerical method of solving the problem of acoustic wave radiation in the presence of a rigid scatterer is described. It combines the finite element method and the boundary algebraic equations. In the proposed method, the exterior domain…

We study distributed algorithms for expected loss minimization where the datasets are large and have to be stored on different machines. Often we deal with minimizing the average of a set of convex functions where each function is the…

Some novel numerical approaches to solving direct and inverse obstacle scattering problems (IOSP) are presented. Scattering by finite obstacles and by periodic structures is considered. The emphasis for solving direct scattering problem is…

Resonant elastic x-ray scattering (REXS) is an exquisite element-sensitive tool for the study of subtle charge, orbital, and spin superlattice orders driven by the valence electrons, which therefore escape detection in conventional x-ray…

We solve the radiative transfer equation (RTE) in anisotropically scattering media as an infinite series. Each series term represents a distinct number of scattering events, with analytical solutions derived for zero and single scattering.…