Related papers: Curvature calculations for the level-set method

In this paper, a methodology for modelling two-phase flows based on a conservative level set method in the framework of finite volume method is presented. The novelty of the interface capturing method used here lies on the advection of…

We present a new method for stochastic shape optimisation of engineering structures. The method generalises an existing deterministic scheme, in which the structure is represented and evolved by a level-set method coupled with mathematical…

In this paper, we propose a new two-dimensional directional discrete wavelet transform that can decompose an image into 12 multiscale directional edge components. The proposed transform is designed in a fully discrete setting and thus is…

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…

We apply convex regularization techniques to the problem of calibrating the local volatility surface model of Dupire taking into account the practical requirement of discrete grids and noisy data. Such requirements are the consequence of…

For an unknown continuous distribution on a real line, we consider the approximate estimation by the discretization. There are two methods for the discretization. First method is to divide the real line into several intervals before taking…

We explore a new way to handle flux boundary conditions imposed on level sets. The proposed approach is a diffuse interface version of the shifted boundary method (SBM) for continuous Galerkin discretizations of conservation laws in…

Bilevel optimization is a powerful tool for many machine learning problems, such as hyperparameter optimization and meta-learning. Estimating hypergradients (also known as implicit gradients) is crucial for developing gradient-based methods…

We show that the theory of varifolds can be suitably enriched to open the way to applications in the field of discrete and computational geometry. Using appropriate regularizations of the mass and of the first variation of a varifold we…

Bilevel optimization has been developed for many machine learning tasks with large-scale and high-dimensional data. This paper considers a constrained bilevel optimization problem, where the lower-level optimization problem is convex with…

Symmetry preserving difference schemes approximating second and third order ordinary differential equations are presented. They have the same three or four-dimensional symmetry groups as the original differential equations. The new…

When dealing with continuous numeric features, we usually adopt feature discretization. In this work, to find the best way to conduct feature discretization, we present some theoretical analysis, in which we focus on analyzing correctness…

Neural network quantization has become an important research area due to its great impact on deployment of large models on resource constrained devices. In order to train networks that can be effectively discretized without loss of…

Seeking the convex hull of an object is a very fundamental problem arising from various tasks. In this work, we propose two variational convex hull models using level set representation for 2-dimensional data. The first one is an exact…

Microvascular networks are challenging to model because these structures are currently near the diffraction limit for most advanced three-dimensional imaging modalities, including confocal and light sheet microscopy. This makes semantic…

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).…

This paper investigates a discretization scheme for mean curvature motion on point cloud varifolds with particular emphasis on singular evolutions. To define the varifold a local covariance analysis is applied to compute an approximate…

A method is introduced for the construction of meshless discretization schemes which preserve Lie symmetries of the differential equations that these schemes approximate. The method exploits the fact that equivariant moving frames provide a…

This paper studies the characteristics and applicability of the CutFEM approach as the core of a robust topology optimization framework for 3D laminar incompressible flow and species transport problems at low Reynolds number (Re < 200).…

For elliptic interface problems with discontinuous coefficients, the maximum accuracy order for compact 9-point finite difference scheme in irregular points is three [7]. The discontinuous coefficients usually have abrupt jumps across the…