Related papers: Naturally curved quadrilateral mesh generation usi…

In contrast to the somewhat abstract, group theoretical approach adopted by many papers, our work provides a new and more intuitive derivation of steerable convolutional neural networks in $d$ dimensions. This derivation is based on…

We introduce a smoothing algorithm for triangle, quadrilateral, tetrahedral and hexahedral meshes whose centerpiece is a simple geometric triangle transformation. The first part focuses on the mathematical properties of the element…

Deep generative models have shown success in generating 3D shapes with different representations. In this work, we propose Neural Volumetric Mesh Generator(NVMG) which can generate novel and high-quality volumetric meshes. Unlike the…

High-quality mesh generation is the foundation of accurate finite element analysis. Due to the vast interior vertices search space and complex initial boundaries, mesh generation for complicated domains requires substantial manual…

This paper presents a method to generate valid high order meshes with optimized geometrical accuracy. The high order meshing procedure starts with a linear mesh, that is subsequently curved without taking care of the validity of the high…

We analyse the local discontinuous Galerkin (LDG) method for two-dimensional singularly perturbed reaction-diffusion problems. A class of layer-adapted meshes, including Shishkin- and Bakhvalov-type meshes, is discussed within a general…

With the discovery of self-accelerating beams, possibility of obtaining curved light beams in free space has been realized. These special beams paved the way for many new applications as well as the exploration of novel beam types.…

Articulated 3D object generation is fundamental for creating realistic, functional, and interactable virtual assets which are not simply static. We introduce MeshArt, a hierarchical transformer-based approach to generate articulated 3D…

Traditional methods for high-dimensional diffeomorphic mapping often struggle with the curse of dimensionality. We propose a mesh-free learning framework designed for $n$-dimensional mapping problems, seamlessly combining variational…

Cross fields play a critical role in various geometry processing tasks, especially for quad mesh generation. Existing methods for cross field generation often struggle to balance computational efficiency with generation quality, using slow…

We present a robust and efficient target-based mesh adaptation methodology, building on hybridized discontinuous Galerkin schemes for (nonlinear) convection-diffusion problems, including the compressible Euler and Navier-Stokes equations.…

We present a new approach to using neural networks to approximate the solutions of variational equations, based on the adaptive construction of a sequence of finite-dimensional subspaces whose basis functions are realizations of a sequence…

We introduce a distributed adaptive quadrature method that formulates multidimensional integration as a hierarchical domain decomposition problem on multi-GPU architectures. The integration domain is recursively partitioned into subdomains…

The generation of triangle meshes from point clouds, i.e. meshing, is a core task in computer graphics and computer vision. Traditional techniques directly construct a surface mesh using local decision heuristics, while some recent methods…

In this work, we propose an extension of the mixed Virtual Element Method (VEM) for bi-dimensional computational grids with curvilinear edge elements. The approximation by means of rectilinear edges of a domain with curvilinear geometrical…

In this paper, based on the combination of finite element mesh and neural network, a novel type of neural network element space and corresponding machine learning method are designed for solving partial differential equations. The…

We propose and demonstrate a generative deep learning approach for the shape recognition of an arbitrary object from its acoustic scattering properties. The strategy exploits deep neural networks to learn the mapping between the latent…

High-order methods offer superior dispersion and dissipation properties compared to low-order schemes but require robust stabilization for discontinuities. To ensure stability, local artificial viscosity is common, but often degrades…

All-dielectric metasurfaces exhibit exotic electromagnetic responses, similar to those obtained with metal-based metamaterials. Research in all-dielectric metasurfaces currently uses relatively simple unit-cell designs, but increased…

This paper is concerned with the design of two different classes of Galerkin boundary element methods for the solution of high-frequency sound-hard scattering problems in the exterior of two-dimensional smooth convex scatterers. Both…