Related papers: A locally gradient-preserving reinitialization for…

In this paper we consider a level set reinitialization technique based on a high-order, local discontinuous Galerkin method on unstructured triangular meshes. A finite volume based subcell stabilization is used to improve the nonlinear…

The level set method is a widely used tool for solving reachability and invariance problems. However, some shortcomings, such as the difficulties of handling dissipation function and constructing terminal conditions for solving the…

The level-set method is a popular method for interface capturing. One of the advantages of the level-set method is that the curvature and the normal vector of the interface can be readily calculated from the level-set function. However, in…

We introduce a level set based approach to Bayesian geometric inverse problems. In these problems the interface between different domains is the key unknown, and is realized as the level set of a function. This function itself becomes the…

This paper proposes a Cartesian grid-based boundary integral method for efficiently and stably solving two representative moving interface problems, the Hele-Shaw flow and the Stefan problem. Elliptic and parabolic partial differential…

The linear transport equation allows to advect level-set functions to represent moving sharp interfaces in multiphase flows as zero level-sets. A recent development in computational fluid dynamics is to modify the linear transport equation…

In this paper, we introduce a novel way to represent the interface for two-phase flows with phase change. We combine a level-set method with a Cartesian embedded boundary method and take advantage of both. This is part of an effort to…

A numerical investigation of grain-boundary grooving by means of a Level Set method is carried out. An idealized polygranular interconnect which consists of grains separated by parallel grain boundaries aligned normal to the average…

The classical level set method, which represents the boundary of the unknown geometry as the zero-level set of a function, has been shown to be very effective in solving shape optimization problems. The present work addresses the issue of…

This paper proposes a deep-learning-based method for recovering a signed distance function (SDF) of a given hypersurface represented by an implicit level set function. Using the flexibility of constructing a neural network, we use an…

In this paper, we propose a novel gradient recovery method for elliptic interface problem using body-fitted mesh in two dimension. Due to the lack of regularity of solution at interface, standard gradient recovery methods fail to give…

In this paper we introduce discrete gradient methods to discretize irreversible port-Hamiltonian systems showing that the main qualitative properties of the continuous system are preserved using this kind discretizations methods.

A finite element method is introduced to track interface evolution governed by the level set equation. The method solves for the level set indicator function in a narrow band around the interface. An extension procedure, which is essential…

Training neural networks with reinforcement learning (RL) typically relies on backpropagation (BP), necessitating storage of activations from the forward pass for subsequent backward updates. Furthermore, backpropagating error signals…

For decades, the computational multiphase flow community has grappled with mass loss in the level set method. Numerous solutions have been proposed, from fixing the reinitialization step to combining the level set method with other…

In this paper we propose a novel regularization strategy for the local discontinuous Galerkin method to solve the Hamilton-Jacobi equation in the context of level-set reinitialization. The novel regularization idea works in analogy to…

The present work illustrates a difficulty with the level-set method to accurately capture the curvature of interfaces in regions that are of equal distance to two or more interfaces. Such regions are characterized by kinks in the level-set…

In this paper, a parametric level set method for reconstruction of obstacles in general inverse problems is considered. General evolution equations for the reconstruction of unknown obstacles are derived in terms of the underlying level set…

Bilevel optimization enjoys a wide range of applications in emerging machine learning and signal processing problems such as hyper-parameter optimization, image reconstruction, meta-learning, adversarial training, and reinforcement…

This paper proposes localized subspace iteration (LSI) methods to construct generalized finite element basis functions for elliptic problems with multiscale coefficients. The key components of the proposed method consist of the localization…