Related papers: A conservative, consistent, and scalable meshfree …
As Artificial Intelligence models, such as Large Video-Language models (VLMs), grow in size, their deployment in real-world applications becomes increasingly challenging due to hardware limitations and computational costs. To address this,…
This paper is part of a program to combine a staggered time and staggered spatial discretization of continuum mechanics problems so that any property of the continuum that is proved using vector calculus can be proven in an analogous way…
We present a novel hybrid computational method to simulate accurately dendritic solidification in the low undercooling limit where the dendrite tip radius is one or more orders of magnitude smaller than the characteristic spatial scale of…
In this paper we shall introduce a simple, effective numerical method for finding differential operators for scalar and vector-valued functions on surfaces. The key idea of our algorithm is to develop an intrinsic and unified way to compute…
High-dimensional data are often assumed to lie on lower-dimensional manifolds. We study how to construct diffusion processes on this data manifold using only point cloud samples and without access to charts, projections, or other geometric…
Current mesh reduction techniques, while numerous, all primarily reduce mesh size by successive element deletion (e.g. edge collapses) with the goal of geometric and topological feature preservation. The choice of geometric error used to…
This paper introduces a novel method for reconstructing meshes from sparse point clouds by predicting edge connection. Existing implicit methods usually produce superior smooth and watertight meshes due to the isosurface extraction…
In this paper we present a new high order semi-implicit DG scheme on two-dimensional staggered triangular meshes applied to different nonlinear systems of hyperbolic conservation laws such as advection-diffusion models, incompressible…
We propose a new method for fine registering multiple point clouds simultaneously. The approach is characterized by being dense, therefore point clouds are not reduced to pre-selected features in advance. Furthermore, the approach is robust…
As two fundamental representation modalities of 3D objects, 3D point clouds and multi-view 2D images record shape information from different domains of geometric structures and visual appearances. In the current deep learning era,…
The first paper of this series presents a discretely entropy stable discontinuous Galerkin (DG) method for the resistive magnetohydrodynamics (MHD) equations on three-dimensional curvilinear unstructured hexahedral meshes. Compared to other…
We present a meshfree collocation scheme to discretize intrinsic surface differential operators over scalar fields on smooth curved surfaces with given normal vectors and a non-intersecting tubular neighborhood. The method is based on…
In the rapidly evolving field of 3D reconstruction, 3D Gaussian Splatting (3DGS) and 2D Gaussian Splatting (2DGS) represent significant advancements. Although 2DGS compresses 3D Gaussian primitives into 2D Gaussian surfels to effectively…
Denoising diffusion models have demonstrated outstanding results in 2D image generation, yet it remains a challenge to replicate its success in 3D shape generation. In this paper, we propose leveraging multi-view depth, which represents…
Numerical methods for hyperbolic PDEs require stabilization. For linear acoustics, divergence-free vector fields should remain stationary, but classical Finite Difference methods add incompatible diffusion that dramatically restricts the…
In this paper, we revisit multimodal few-shot 3D point cloud semantic segmentation (FS-PCS), identifying a conflict in "Fuse-then-Refine" paradigms: the "Plasticity-Stability Dilemma." In addition, CLIP's inter-class confusion can result in…
Detecting changes is of fundamental importance when analyzing data streams and has many applications, e.g., in predictive maintenance, fraud detection, or medicine. A principled approach to detect changes is to compare the distributions of…
We present a cut finite element method for the heat equation on two overlapping meshes: a stationary background mesh and an overlapping mesh that evolves inside/"on top" of it. Here the overlapping mesh is prescribed a simple discontinuous…
Despite the remarkable success of deep learning, an optimal convolution operation on point clouds remains elusive owing to their irregular data structure. Existing methods mainly focus on designing an effective continuous kernel function…
Algebraically stabilized finite element discretizations of scalar steady-state convection-diffusion-reaction equations often provide accurate approximate solutions satisfying the discrete maximum principle (DMP). However, it was observed…