Related papers: An Interface Tracking Method with Triangle Edge Cu…
The paper develops a hybrid method for solving a system of advection--diffusion equations in a bulk domain coupled to advection--diffusion equations on an embedded surface. A monotone nonlinear finite volume method for equations posed in…
We consider discrete Poisson interface problems resulting from linear unfitted finite elements, also called cut finite elements (CutFEM). Three of these unfitted finite element methods known from the literature are studied. All three…
A virtual element method (VEM) with the first order optimal convergence order is developed for solving two-dimensional Maxwell interface problems on a special class of polygonal meshes that are cut by the interface from a background…
Real-time 3D reconstruction from RGB-D sensor data plays an important role in many robotic applications, such as object modeling and mapping. The popular method of fusing depth information into a truncated signed distance function (TSDF)…
Multiphase, compressible and viscous flows are of crucial importance in a wide range of scientific and engineering problems. Despite the large effort paid in the last decades to develop accurate and efficient numerical techniques to address…
3D shape analysis is an important research topic in computer vision and graphics. While existing methods have generalized image-based deep learning to meshes using graph-based convolutions, the lack of an effective pooling operation…
Mesh adaptivity is a useful tool for efficient solution to partial differential equations in very complex geometries. In the present paper we discuss the use of polygonal mesh refinement in order to tackle two common issues: first,…
In this paper, we propose a simple and accurate numerical method for capturing moving interfaces on fixed Eulerian grids by coupling the Tangent of Hyperbola Interface Capturing (THINC) method and Level Set (LS) method. The innovative and…
The vast majority of mesh-based modelling applications iteratively transform the mesh vertices under prescribed geometric conditions. This occurs in particular in methods cycling through the constraint set such as Position-Based Dynamics…
In this work, we present a dense tracking and mapping system named Vox-Fusion, which seamlessly fuses neural implicit representations with traditional volumetric fusion methods. Our approach is inspired by the recently developed implicit…
An important step in shape optimization with partial differential equation constraints is to adapt the geometry during each optimization iteration. Common strategies are to employ mesh-deformation or re-meshing, where one or the other…
We develop a family of cut finite element methods of different orders based on the discontinuous Galerkin framework, for hyperbolic conservation laws with stationary interfaces in both one and two space dimensions, and for moving interfaces…
Existing learning-based methods for point cloud rendering adopt various 3D representations and feature querying mechanisms to alleviate the sparsity problem of point clouds. However, artifacts still appear in rendered images, due to the…
We present a Cartesian cut-cell finite-volume method for sharp-interface two-phase diffusion problems in static geometries. The formulation follows a two-fluid approach: independent diffusion equations are discretized in each phase on a…
Mesh simplification is the process of reducing the number of vertices, edges and triangles in a three-dimensional (3D) mesh while preserving the overall shape and salient features of the mesh. A popular strategy for this is edge collapse,…
Fluid flow applications can involve a number of coupled problems. One is the simulation of free-surface flows, which require the solution of a free-boundary problem. Within this problem, the governing equations of fluid flow are coupled…
This work develops and analyzes a variational-monolithic unfitted finite element formulation of a linear fluid-structure interaction problem in Eulerian coordinates with a fixed interface. The overall discretization is based on a backward…
A novel interface reconstruction strategy for volume of fluid (VOF) methods is introduced that represents the liquid-gas interface as two planes that co-exist within a single computational cell. In comparison to the piecewise linear…
The dynamics of compressible liquid-vapor flow depends sensitively on the microscale behavior at the phase boundary. We consider a sharp-interface approach, and propose a multiscale model to describe liquid-vapor flow accurately, without…
This work proposes a novel variational approximation of partial differential equations on moving geometries determined by explicit boundary representations. The benefits of the proposed formulation are the ability to handle large…