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This paper proposes a rational filtering domain decomposition technique for the solution of large and sparse symmetric generalized eigenvalue problems. The proposed technique is purely algebraic and decomposes the eigenvalue problem…
We solve the classic albedo and Milne problems of plane-parallel illumination of an isotropically-scattering half-space when generalized to a Euclidean domain $\mathbb{R}^d$ for arbitrary $d \ge 1$. A continuous family of pseudo-problems…
Radiative transfer simulations are now at the forefront of numerical astrophysics. They are becoming crucial for an increasing number of astrophysical and cosmological problems; at the same time their computational cost has come to the…
We present a new numerical approach that is able to solve the multi-dimensional radiative transfer equations in all opacity regimes on a Lagrangian, unstructured network of characteristics based on a stochastic point process. Our method…
Numerical methods for radiative transfer play a key role in modern-day astrophysics and cosmology, including study of the inhomogeneous reionization process. In this context, ray tracing methods are well-regarded for accuracy but notorious…
Recent advances in random-walk particle-tracking have enabled direct simulation of mixing and reactions on particles by allowing the particles to interact with each other using a multi-point mass transfer scheme. The mass transfer scheme…
A novel inter-frame coding approach to the problem of varying channel-state conditions in broadcast wireless communication is developed in this paper; this problem causes the appropriate code-rate to vary across different transmitted frames…
In this work, we consider alternative discretizations for PDEs which use expansions involving integral operators to approximate spatial derivatives. These constructions use explicit information within the integral terms, but treat boundary…
In this paper we generalize and improve a recently developed domain decomposition preconditioner for the iterative solution of discretized Helmholtz equations. We introduce an improved method for transmission at the internal boundaries…
We present the RAW domain diffusion model (RDDM), an end-to-end diffusion model that restores photo-realistic images directly from the sensor RAW data. While recent sRGB-domain diffusion methods achieve impressive results, they are caught…
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…
Accurate and fast modeling of electric fields in layered structures have a great scientific and practical value. Prevalent method for that is transfer-matrix method. However, transfer matrix method is limited to infinite plane wave…
We describe an important addition to the parallel implementation of our generalized NLTE stellar atmosphere and radiative transfer computer program PHOENIX. In a previous paper in this series we described data and task parallel algorithms…
To study the temperature in a gas subjected to electromagnetic radiations, one may use the Radiative Transfer equations coupled with the Navier-Stokes equations. The problem has 7 dimensions; however with minimal simplifications it is…
We study analogical trajectory transfer, where the goal is to translate motion trajectories in one 3D environment to a semantically analogous location in another. Such a capacity would enable machines to perform analogical spatial…
We shall derive and propose several efficient overlapping domain decomposition methods for solving some typical linear inverse problems, including the identiffication of the flux, the source strength and the initial temperature in second…
Fast, reliable shape reconstruction is an essential ingredient in many computer vision applications. Neural Radiance Fields demonstrated that photorealistic novel view synthesis is within reach, but was gated by performance requirements for…
We introduce an optimisation method for variational quantum algorithms and experimentally demonstrate a 100-fold improvement in efficiency compared to naive implementations. The effectiveness of our approach is shown by obtaining…
The Easy Path Wavelet Transform is an adaptive transform for bivariate functions (in particular natural images) which has been proposed in [1]. It provides a sparse representation by finding a path in the domain of the function leveraging…
We develop innovative algorithms for solving the strong-constraint formulation of four-dimensional variational data assimilation in large-scale applications. We present a space-time decomposition approach that employs domain decomposition…