Related papers: A linear MARS method for three-dimensional interfa…
Most LiDAR odometry and SLAM systems construct maps in point clouds, which are discrete and sparse when zoomed in, making them not directly suitable for navigation. Mesh maps represent a dense and continuous map format with low memory…
This paper introduces the MeshAC package, which generates three-dimensional adaptive meshes tailored for the efficient and robust implementation of multiscale coupling methods. While Delaunay triangulation is commonly used for mesh…
New finite element methods are proposed for elliptic interface problems in one and two dimensions. The main motivation is not only to get an accurate solution but also an accurate first order derivative at the interface (from each side).…
We present a novel approach to morph between two isometric poses of the same non-rigid object given as triangular meshes. We model the morphs as linear interpolations in a suitable shape space $\mathcal{S}$. For triangulated 3D polygons, we…
The level-set method is a popular interface tracking method in two-phase flow simulations. An often-cited reason for using it is that the method naturally handles topological changes in the interface, e.g. merging drops, due to the implicit…
In this paper, we propose an approach for solving PDEs on evolving surfaces using a combination of the trace finite element method and a fast marching method. The numerical approach is based on the Eulerian description of the surface…
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…
Along with the fast evolution of deep neural networks, the hardware system is also developing rapidly. As a promising solution achieving high scalability and low manufacturing cost, multi-accelerator systems widely exist in data centers,…
We address the problem of human motion tracking by registering a surface to 3-D data. We propose a method that iteratively computes two things: Maximum likelihood estimates for both the kinematic and free-motion parameters of a kinematic…
We present a novel shape-approximating anisotropic re-meshing algorithm as a geometric generalization of the adaptive moving mesh method. Conventional moving mesh methods reduce the interpolation error of a mesh that discretizes a given…
Reconstruction of object or scene surfaces has tremendous applications in computer vision, computer graphics, and robotics. In this paper, we study a fundamental problem in this context about recovering a surface mesh from an implicit field…
Tracking objects in 3D space and predicting their 6DoF pose is an essential task in computer vision. State-of-the-art approaches often rely on object texture to tackle this problem. However, while they achieve impressive results, many…
A new higher-order accurate method is proposed that combines the advantages of the classical $p$-version of the FEM on body-fitted meshes with embedded domain methods. A background mesh composed by higher-order Lagrange elements is used.…
We study the problem of approximating a surface $F$ in $R^3$ by a high quality mesh, a piecewise-flat triangulated surface whose triangles are as close as possible to equilateral. The MidNormal algorithm generates a triangular mesh that is…
This paper extends the author's previous two-dimensional work with Ou and LeVeque to high-resolution finite volume modeling of systems of fluids and poroelastic media in three dimensions, using logically rectangular mapped grids. A method…
Accurate numerical simulation of material extrusion additive manufacturing requires reliable tracking of evolving material interfaces while preserving mass conservation. Inaccurate mass conservation can lead to significant discrepancies…
The sparse representation of signals defined on Euclidean domains has been successfully applied in signal processing. Bringing the power of sparse representations to non-regular domains is still a challenge, but promising approaches have…
A prerequisite for many biomechanical simulation techniques is discretizing a bounded volume into a tetrahedral mesh. In certain contexts, such as cortical surface simulations, preserving input surface connectivity is critical. However,…
The 3D Gaussian Splatting (3DGS)-based SLAM system has garnered widespread attention due to its excellent performance in real-time high-fidelity rendering. However, in real-world environments with dynamic objects, existing 3DGS-based SLAM…
We present a compatible space-time hybridizable/embedded discontinuous Galerkin discretization for nonlinear free-surface waves. We pose this problem in a two-fluid (liquid and gas) domain and use a time-dependent level-set function to…