Related papers: Automatic surface mesh generation for discrete mod…
This paper presents an immersed, isogeometric finite element framework to predict the response of multi-material, multi-physics problems with complex geometries using locally refined discretizations. To circumvent the need to generate…
Curved structures in soft matter and biological systems commonly emerge as a result of self-assembly processes where building blocks aggregate in a controlled manner, giving rise to specific system structure and properties. Learning how to…
Recent probabilistic methods for 3D triangular meshes capture diverse shapes by differentiable mesh connectivity, but face high computational costs with increased shape details. We introduce a new differentiable mesh processing method that…
In this report, we introduce UltraShape 1.0, a scalable 3D diffusion framework for high-fidelity 3D geometry generation. The proposed approach adopts a two-stage generation pipeline: a coarse global structure is first synthesized and then…
We present a computational approach for unfolding 3D shapes isometrically into the plane as a single patch without overlapping triangles. This is a hard, sometimes impossible, problem, which existing methods are forced to soften by allowing…
We show that by extending the Laplacian formalism, which was first introduced in the Graphics community to regularize 3D meshes, we can turn the monocular 3D shape reconstruction of a deformable surface given correspondences with a…
Particle discretizations of partial differential equations are advantageous for high-dimensional kinetic models in phase space due to their better scalability than continuum approaches with respect to dimension. Complex processes…
In the field of topology optimization, the homogenization approach has been revived as an important alternative to the established, density-based methods because it can represent the microstructural design at a much finer length-scale than…
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…
This work develops a framework to create meshes with user-specified homology from potentially dirty geometry by coupling background grids, persistent homology, and a generalization of volume fractions. For a mesh with fixed grid size, the…
We prove that a planar $C^2$-regular boundary $\Gamma$ can always be parameterized with its closest point projection $\pi$ over a certain collection of edges $\Gamma_h$ in an ambient triangulation, by making simple assumptions on the…
In this paper, we present an automated pipeline for generating domain-specific synthetic datasets with diffusion models, addressing the distribution shift between pre-trained models and real-world deployment environments. Our three-stage…
We consider the reliable implementation of high-order unfitted finite element methods on Cartesian meshes with hanging nodes for elliptic interface problems. We construct a reliable algorithm to merge small interface elements with their…
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…
The approaches taken to describe and develop spatial discretisations of the domains required for geophysical simulation models are commonly ad hoc, model or application specific and under-documented. This is particularly acute for…
We present a novel approach for generating isotropic surface triangle meshes directly from unoriented 3D point clouds, with the mesh density adapting to the estimated local feature size (LFS). Popular reconstruction pipelines first…
The finite element method (FEM) has several computational steps to numerically solve a particular problem, to which many efforts have been directed to accelerate the solution stage of the linear system of equations. However, the finite…
This paper describes a method for fast simplification of surface meshes. Whereas past methods focus on visual appearance, our goal is to solve equations on the surface. Hence, rather than approximate the extrinsic geometry, we construct a…
In this paper, we propose a novel meshfree Generalized Finite Difference Method (GFDM) approach to discretize PDEs defined on manifolds. Derivative approximations for the same are done directly on the tangent space, in a manner that mimics…
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…