Related papers: Near optimal angular quadratures for polarised rad…
Modeling spectral line profiles taking frequency redistribution effects into account is a notoriously challenging problem from the computational point of view, especially when polarization phenomena (atomic polarization and polarized…
We consider the iterative solution of anisotropic radiative transfer problems using residual minimization over suitable subspaces. We show convergence of the resulting iteration using Hilbert space norms, which allows us to obtain…
We examine sparse grid quadrature on weighted tensor products (WTP) of reproducing kernel Hilbert spaces on products of the unit sphere, in the case of worst case quadrature error for rules with arbitrary quadrature weights. We describe a…
This paper presents a new progressive compression method for triangular meshes. This method, in fact, is based on a schema of irregular multi-resolution analysis and is centered on the optimization of the rate-distortion trade-off. The…
The alternating least squares algorithm for CP and Tucker decomposition is dominated in cost by the tensor contractions necessary to set up the quadratic optimization subproblems. We introduce a novel family of algorithms that uses…
We present benchmark problems and solutions for the continuum radiative transfer (RT) in a 2D disk configuration. The reliability of three Monte-Carlo and two grid-based codes is tested by comparing their results for a set of well-defined…
Context. Magnetic fields are important to the dynamics of many astrophysical processes and can typically be studied through polarization observations. Polarimetric interferometry capabilities of modern (sub)millimeter telescope facilities…
High-dimensional sparse data emerge in many critical application domains such as healthcare and cybersecurity. To extract meaningful insights from massive volumes of these multi-dimensional data, scientists employ unsupervised analysis…
We discuss the problem of polarized radiative transfer in general relativity. We present a set of equations suitable for solving the problem numerically for the case of an arbitrary space-time metric, and show numerical solutions to example…
3D Gaussian Splatting (3DGS) has become a leading technique for real-time neural rendering and 3D scene reconstruction, but its rendering cost remains too high for many latency-sensitive scenarios. In particular, the rasterization stage in…
Anisotropic mesh adaptation is studied for linear finite element solution of 3D anisotropic diffusion problems. The M-uniform mesh approach is used, where an anisotropic adaptive mesh is generated as a uniform one in the metric specified by…
The Cartesian coordinate system is the most commonly used system in computer visualization. This is due to its ease of use and processing speed. However, it is not always suitable for a given problem. Angular measures often allow us to…
The transition-matrix ($T$-matrix) approach provides a general formalism to study scattering problems in various areas of physics, including acoustics (scalar fields) and electromagnetics (vector fields), and is related to the theory of the…
In this era of big data, data analytics and machine learning, it is imperative to find ways to compress large data sets such that intrinsic features necessary for subsequent analysis are not lost. The traditional workhorse for data…
Transfer matrices and matrix product operators play an ubiquitous role in the field of many body physics. This paper gives an ideosyncratic overview of applications, exact results and computational aspects of diagonalizing transfer matrices…
We present novel fully-symmetric quadrature rules with positive weights and strictly interior nodes of degrees up to 84 on triangles and 40 on tetrahedra. Initial guesses for solving the nonlinear systems of equations needed to derive…
A direct numerical solution of the radiative transfer equation or any kinetic equation is typically expensive, since the radiative intensity depends on time, space and direction. An expansion in the direction variables yields an equivalent…
Layer potentials represent solutions to partial differential equations in an integral equation formulation. When numerically evaluating layer potentials at evaluation points close to the domain boundary, specialized quadrature techniques…
The thermal radiative transfer (TRT) equations form an integro-differential system that describes the propagation and collisional interactions of photons. Computing accurate and efficient numerical solutions TRT are challenging for several…
For three-dimensional (3D) magnetic objects with linear size $L$ exceeding a few exchange lengths, the micromagnetic state exhibits pronounced informational sparsity: low-dimensional, high-gradient regions (e.g., domain walls) coexist with…