Related papers: Automatic surface mesh generation for discrete mod…
In this paper, gradient-based optimization methods are combined with finite-element modeling for improving electric devices. Geometric design parameters are considered by affine decomposition of the geometry or by the design element…
We present a new high order finite element method for the discretization of partial differential equations on stationary smooth surfaces which are implicitly described as the zero level of a level set function. The discretization is based…
The I-patch is a multi-sided surface representation, defined as a combination of implicit ribbon and bounding surfaces, whose pairwise intersections determine the natural boundaries of the patch. Our goal is to show how a collection of…
Many tasks in geometry processing are modeled as variational problems solved numerically using the finite element method. For solid shapes, this requires a volumetric discretization, such as a boundary conforming tetrahedral mesh.…
Consider the Poisson equation with the Dirichlet boundary condition on a three-dimensional polyhedral domain. For singular solutions from the non-smoothness of the domain boundary, we propose new anisotropic tetrahedral mesh refinement…
Obtaining high-quality particle distributions for stable and accurate particle-based simulations poses significant challenges, especially for complex geometries. We introduce a preprocessing technique for 2D and 3D geometries, optimized for…
In the present work we introduce a novel refinement algorithm for two-dimensional elliptic partial differential equations discretized with Virtual Element Method (VEM). The algorithm improves the numerical solution accuracy and the mesh…
We present 2-D, 3-D, and spherical mesh generators for the Finite Element Method (FEM) using triangular and tetrahedral elements. The mesh nodes are treated as if they were linked by virtual springs that obey Hooke's law. Given the desired…
The 3D mesh is an important representation of geometric data. In the generation of mesh data, geometric deficiencies (e.g., duplicate elements, degenerate faces, isolated vertices, self-intersection, and inner faces) are unavoidable and may…
An extension of the Method of Regularized Stokeslets (MRS) in three dimensions is developed for triangulated surfaces with a piecewise linear force distribution. The method extends the regularized Stokeslet segment methodology used for…
Recent mesh generation approaches typically tokenize triangle meshes into sequences of tokens and train autoregressive models to generate these tokens sequentially. Despite substantial progress, such token sequences inevitably reuse…
In this paper we design efficient quadrature rules for finite element discretizations of nonlocal diffusion problems with compactly supported kernel functions. Two of the main challenges in nonlocal modeling and simulations are the…
In this paper, we consider a time-dependent discrete network model with highly varying connectivity. The approximation by time is performed using an implicit scheme. We propose the coarse scale approximation construction of network models…
Designs generated by density-based topology optimization (TO) exhibit jagged and/or smeared boundaries, which forms an obstacle to their integration with existing CAD tools. Addressing this problem by smoothing or manual design adjustments…
To produce cartographic maps, simplification is typically used to reduce complexity of the map to a legible level. With schematic maps, however, this simplification is pushed far beyond the legibility threshold and is instead constrained by…
Coarse grid projection (CGP) methodology is a novel multigrid method for systems involving decoupled nonlinear evolution equations and linear elliptic Poisson equations. The nonlinear equations are solved on a fine grid and the linear…
Geometric Deep Learning has recently made striking progress with the advent of continuous deep implicit fields. They allow for detailed modeling of watertight surfaces of arbitrary topology while not relying on a 3D Euclidean grid,…
We consider the task of generating realistic 3D shapes, which is useful for a variety of applications such as automatic scene generation and physical simulation. Compared to other 3D representations like voxels and point clouds, meshes are…
This paper deals with shape irregularity issues in discrete topology optimization algorithms whereby the design is created using the automated distribution of material in the design region. Graph theory is employed to derive appropriate…
Meshes are widely used in 3D computer vision and graphics, but their irregular topology poses challenges in applying them to existing neural network architectures. Recent advances in mesh neural networks turn to remeshing and push the…