Related papers: High quality mesh generation using cross and aster…
Meshing of geometric domains having curved boundaries by affine simplices produces a polytopial approximation of those domains. The resulting error in the representation of the domain limits the accuracy of finite element methods based on…
Recent advancements in Radiance Fields have significantly improved novel-view synthesis. However, in many real-world applications, the more advanced challenge lies in inverse rendering, which seeks to derive the physical properties of a…
We present and analyze a new finite element method for solving interface problems on a triangular grid. The method locally modifies a given triangulation such that the interfaces are accurately resolved and the maximal angle condition…
In this paper we propose a method to generate suitably refined finite element meshes using neural networks. As a model problem we consider a linear elasticity problem on a planar domain (possibly with holes) having a polygonal boundary. We…
A mesh improvement methodology is pre- sented which aims to improve the quality of the worst elements in 3D meshes with non-planar surfaces which cannot be improved using traditional methods. A nu- merical optimisation algorithm, which…
A new concept for the higher-order accurate approximation of partial differential equations on manifolds is proposed where a surface mesh composed by higher-order elements is automatically generated based on level-set data. Thereby, it…
Three-dimensional (3-D) meshes are commonly used to represent virtual surfaces and volumes. Over the past decade, 3-D meshes have emerged in industrial, medical, and entertainment applications, being of large practical significance for 3-D…
A fundamental problem in the texturing of 3D meshes using pre-trained text-to-image models is to ensure multi-view consistency. State-of-the-art approaches typically use diffusion models to aggregate multi-view inputs, where common issues…
In this work, we present a boundary and hole detection approach that traverses all the boundaries of an edge-manifold triangular mesh, irrespectively of the presence of singular vertices, and subsequently determines and labels all holes of…
This work presents two integration methods for field transfer in computational aeroacoustics and in coupled field problems, using the finite element method to solve the acoustic field. Firstly, a high-order Gaussian quadrature computes the…
A novel algorithm that produces a quad layout based on imposed set of singularities is proposed. In this paper, we either use singularities that appear naturally, e.g., by minimizing Ginzburg-Landau energy, or use as an input user-defined…
This paper introduces an accurate edge-based smoothed finite element method (ES-FEM) for electromagnetic analysis for both two dimensional cylindrical and three dimensional cartesian systems, which shows much better performance in terms of…
Finite elements of higher continuity, say conforming in $H^2$ instead of $H^1$, require a mapping from reference cells to mesh cells which is continuously differentiable across cell interfaces. In this article, we propose an algorithm to…
Clustering is one of the main tasks in exploratory data analysis and descriptive statistics where the main objective is partitioning observations in groups. Clustering has a broad range of application in varied domains like climate,…
The unprecedented amount and the excellent quality of lensing data that the upcoming ground- and space-based surveys will produce represent a great opportunity to shed light on the questions that still remain unanswered concerning our…
Many time-dependent problems in the field of computational fluid dynamics can be solved using space-time methods. However, such methods can encounter issues with computational cost and robustness. In order to address these issues,…
The field of computer graphics was revolutionized by models such as Neural Radiance Fields and 3D Gaussian Splatting, displacing triangles as the dominant representation for photogrammetry. In this paper, we argue for a triangle comeback.…
The purpose of this research is to describe an efficient iterative method suitable for obtaining high accuracy solutions to high frequency time-harmonic scattering problems. The method allows for both refinement of local polynomial degree…
This paper introduces a novel curve-based slicing method for generating planar layers with dynamically varying orientations in digital light processing (DLP) 3D printing. Our approach effectively addresses key challenges in DLP printing,…
The hybrid high-order method is a modern numerical framework for the approximation of elliptic PDEs. We present here an extension of the hybrid high-order method to meshes possessing curved edges/faces. Such an extension allows us to…