Related papers: An Interface Tracking Method with Triangle Edge Cu…

We present a novel method for calculating interface curvature on 3D unstructured meshes from piecewise-linear interface reconstructions typically generated in the volume of fluid method. Interface curvature is a necessary quantity to…

This paper introduces a novel method for the efficient and accurate computation of volume fractions on unstructured polyhedral meshes, where the phase boundary is an orientable hypersurface, implicitly given as the iso-contour of a…

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…

Polygonal meshes provide an efficient representation for 3D shapes. They explicitly capture both shape surface and topology, and leverage non-uniformity to represent large flat regions as well as sharp, intricate features. This…

Structured output support vector machine (SVM) based tracking algorithms have shown favorable performance recently. Nonetheless, the time-consuming candidate sampling and complex optimization limit their real-time applications. In this…

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…

The number of triangles is a computationally expensive graph statistic which is frequently used in complex network analysis (e.g., transitivity ratio), in various random graph models (e.g., exponential random graph model) and in important…

In this work, we develop a cutting method for solving problems with moving and growing interfaces in 3D. This new method is able to resolve large displacement or deformation of immersed objects by combining the Arbitrary Lagrangian-Eulerian…

From a scalar field defined at the corner of a cube, an isosurface can be extracted using the Marching Cube algorithm. The isosurface separates the cell into two or more partial cells. A similar situation arises when an material interface…

In this work, we present a general, efficient, and provably robust representation for intrinsic triangulations. These triangulations have emerged as a powerful tool for robust geometry processing of surface meshes, taking a low-quality mesh…

In this paper we develop a conservative sharp-interface method dedicated to simulating multiple compressible fluids. Numerical treatments for a cut cell shared by more than two materials are proposed. First, we simplify the interface…

Meshes are ubiquitous in visual computing and simulation, yet most existing machine learning techniques represent meshes only indirectly, e.g. as the level set of a scalar field or deformation of a template, or as a disordered triangle soup…

In this paper, we propose a novel mesh-free numerical method for solving the elliptic interface problems based on deep learning. We approximate the solution by the neural networks and, since the solution may change dramatically across the…

We propose a space-efficient algorithm for hidden surface removal that combines one of the fastest previous algorithms for that problem with techniques based on bit manipulation. Such techniques had been successfully used in other settings,…

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…

We present a finite element discretisation to model the interaction between a poroelastic structure and an elastic medium. The consolidation problem considers fully coupled deformations across an interface, ensuring continuity of…

We introduce a novel offset meshing approach that can robustly handle a 3D surface mesh with an arbitrary geometry and topology configurations, while nicely capturing the sharp features on the original input for both inward and outward…

Geometric rounding of a mesh is the task of approximating its vertex coordinates by floating point numbers while preserving mesh structure. Geometric rounding allows algorithms of computational geometry to interface with numerical…

We develop a new optimisation technique that combines multiresolution subdivision surfaces for boundary description with immersed finite elements for the discretisation of the primal and adjoint problems of optimisation. Similar to wavelets…

The phenomenon of arrest of an unstably-growing crack due to a curved weak interface is investigated. The weak interface can produce the deviation of the crack path, trapping the crack at the interface, leading to stable crack growth for…