Related papers: Multi-resolution unstructured grid-generation for …
Neural rendering techniques, including NeRF and Gaussian Splatting (GS), rely on photometric consistency to produce high-quality reconstructions. However, in real-world scenarios, it is challenging to guarantee perfect photometric…
We construct a new class of complete constant mean curvature surfaces in R^3. These are geometrically different than the surfaces constructed by Kapouleas' gluing technique. These are obtained by piecing together half-Delaunay surfaces to…
We study the problem to provide a triangular form based on implicit differential equations for non-linear multi-input systems with respect to the flatness property. Furthermore, we suggest a constructive method for the transformation of a…
We present FoamGrid, a new implementation of the DUNE grid interface. FoamGrid implements one- and two-dimensional grids in a physical space of arbitrary dimension, which allows for grids for curved domains. Even more, the grids are not…
In this work we present an algorithm to construct an infinitely differentiable smooth surface from an input consisting of a (rectilinear) triangulation of a surface of arbitrary shape. The original surface can have non-trivial genus and…
Many problems in engineering, chemistry and physics require the representation of solutions in complex geometries. In the paper we deal with a problem of unstructured mesh generation for the control volume method. We propose an algorithm…
This paper aims to develop an efficient adaptive finite element method for the second-order elliptic problem. Although the theory for adaptive finite element methods based on residual-type a posteriori error estimator and bisection…
Geophysical model domains typically contain irregular, complex fractal-like boundaries and physical processes that act over a wide range of scales. Constructing geographically constrained boundary-conforming spatial discretizations of these…
We present a novel method for computing the Minkowski Functionals from isodensity surfaces extracted directly from the Delaunay tessellation of a point distribution. This is an important step forward compared to the previous cosmological…
We present the design and implementation details of a geometric multigrid method on adaptively refined meshes for massively parallel computations. The method uses local smoothing on the refined part of the mesh. Partitioning is achieved by…
A novel and scalable geometric multi-level algorithm is presented for the numerical solution of elliptic partial differential equations, specially designed to run with high occupancy of streaming processors inside Graphics Processing…
Computational technologies for the approximate solution of multidimensional boundary value problems often rely on irregular computational meshes and finite-volume approximations. In this framework, the discrete problem represents the…
We present a method for reconstructing triangle meshes from point clouds. Existing learning-based methods for mesh reconstruction mostly generate triangles individually, making it hard to create manifold meshes. We leverage the properties…
In this paper we characterize a function defined on the set of edges of a triangulated surface such that there is a spherical angle structure having the function as the edge invariant (or Delaunay invariant). We also characterize a function…
This article investigates the application of computer vision and graph-based models in solving mesh-based partial differential equations within high-performance computing environments. Focusing on structured, graded structured, and…
This article is the updated version of the paper: "Combined 3D thinning and greedy algorithm to approximate realistic particles with corrected mechanical properties, Granular Matter (2019)" by the first author [58]. The main changes here…
Several multiscale methods account for sub-grid scale features using coarse scale basis functions. For example, in the Multiscale Finite Volume method the coarse scale basis functions are obtained by solving a set of local problems over…
We propose a family of gradient reconstruction schemes based on the solution of over-determined systems by orthogonal or oblique projections. In the case of orthogonal projections, we retrieve familiar weighted least-squares gradients, but…
Scale analysis based on coarse-graining has been proposed recently as an alternative to Fourier analysis. It is now broadly used to analyze energy spectra and energy transfers in eddy-resolving ocean simulations. However, for data from…
We propose a two-stage algorithm for generating Delaunay triangulations in 2D and Delaunay tetrahedra in 3D that employs near maximal Poisson-disk sampling. The method generates a variable resolution mesh in 2- and 3-dimensions in linear…