Related papers: Discrete Quantization on Spherical Geometries: Exp…

We prove that if a complete connected $n$-dimensional Riemannian manifold $M$ has radial sectional curvature at a base point $p\in M$ bounded from below by the radial curvature function of a two-sphere of revolution $\widetilde M$ belonging…

In this paper, we present a unified perspective on sphere consistent truncations based on the classical geometric properties of sphere bundles. The backbone of our approach is the global angular form for the sphere. A universal formula for…

We study the problem of decomposing a volume bounded by a smooth surface into a collection of Voronoi cells. Unlike the dual problem of conforming Delaunay meshing, a principled solution to this problem for generic smooth surfaces remained…

This work extends our previous study from S. Shrestha et al. (2024) by introducing a new abstract framework for Variational Multiscale (VMS) methods at the discrete level. We introduce the concept of what we define as the optimal projector…

The well-known spatial integration schemes in molecular electronic structure theory, immune to cusps and point singularities of some kind at atomic positions, use a set of weighting functions to split the integrand into a sum of…

In this paper, we investigate the optimization of Centroidal Voronoi Tessellations (CVT) under geometric constraints. For this purpose, we minimize a linear combination of the standard CVT energy functional with terms involving geometric…

The simple cubic lattice defines a set of points at regular distances. The volume of the Voronoi cells around each point may serve as a weight for integration over the entire space. We add interstitial points to this grid according to the…

Voronoi grids have been successfully used to represent density structures of gas in astronomical hydrodynamics simulations. While some codes are explicitly built around using a Voronoi grid, others, such as Smoothed Particle Hydrodynamics…

Following our paper [J. Math. Phys. 50 (2009) 123102], we systematically carry out Lie symmetry analysis for the barotropic vorticity equation on the rotating sphere. All finite-dimensional subalgebras of the corresponding maximal Lie…

Finite difference method was extended to unstructured meshes to solve Euler equations. The spatial discretization is made of two steps. First, numerical fluxes are computed at the middle point of each edge with high order accuracy. In this…

Navigating topological transitions in cellular mechanical systems is a significant challenge for existing simulation methods. While abstract models lack predictive capabilities at the cellular level, explicit network representations…

We present a method for generating higher-order finite volume discretizations for Poisson's equation on Cartesian cut cell grids in two and three dimensions. The discretization is in flux-divergence form, and stencils for the flux are…

We introduce optimal quadrature rules for spline spaces that are frequently used in Galerkin discretizations to build mass and stiffness matrices. Using the homotopy continuation concept [6] that transforms optimal quadrature rules from…

We consider the construction of a polyhedral Delaunay partition as a limit of the sequence of power diagrams (radical partitions). The dual Voronoi diagram is obtained as a limit of the sequence of weighted Delaunay partitions. The problem…

We apply an unfitted HDG discretization to a model problem in shape optimization. The method proposed uses a fixed, shape regular, non-geometry conforming mesh and a high order transfer technique to deal with the curved boundaries arising…

Exact solutions of Einstein equations with null Riemman-Christoffel curvature tensor everywhere, except on a hypersurface, are studied using quantum particles obeying the Klein-Gordon equation. We consider the particular cases when the…

A general approach to a solution of few- and many-body scattering problems based on a continuum-discretization procedure is described in detail. The complete discretization of continuous spectrum is realized using stationary wave packets…

We present a new mimetic finite difference method for diffusion problems that converges on grids with \textit{curved} (i.e., non-planar) faces. Crucially, it gives a symmetric discrete problem that uses only one discrete unknown per curved…

We develop a new approach to vector quantization, which guarantees an intrinsic stationarity property that also holds, in contrast to regular quantization, for non-optimal quantization grids. This goal is achieved by replacing the usual…

$D$-optimal designs originate in statistics literature as an approach for optimal experimental designs. In numerical analysis points and weights resulting from maximal determinants turned out to be useful for quadrature and interpolation.…