相关论文: The Augmented Fast Marching Method for Level Set R…

In this paper, a new re-initialization method for the conservative level-set function is put forward. First, it has been shown that the re-initialization and advection equations of the conservative level-set function are mathematically…

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…

It is well-known that the standard level set advection equation does not preserve the signed distance property, which is a desirable property for the level set function representing a moving interface. Therefore, reinitialization or…

Existing artificial compression based reinitialization scheme for conservative level set method has a few drawbacks, like distortion of fluid-fluid interface, unphysical patch formation away from the interface and lack of mass conservation.…

A passively advected sharp interface can be represented as the zero level set of a level set function $f$. The linear transport equation $\partial_tf+v\cdot \nabla f =0$ is the simplest governing equation for such a level set function.…

Time-unconditional generative models learn time-independent denoising vector fields. But without time conditioning, the same noisy input may correspond to multiple noise levels and different denoising directions, which interferes with the…

The level set method commonly requires a reinitialization of the level set function due to interface motion and deformation. We extend the traditional technique for reinitializing the level set function to a method that preserves the…

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.…

This paper presents a simple and highly accurate method for capturing sharp interfaces moving in divergence-free velocity fields using the high-order Flux Reconstruction approach on unstructured grids. A well-known limitation of high-order…

The level set approach represents surfaces implicitly, and advects them by evolving a level set function, which is numerically defined on an Eulerian grid. Here we present an approach that augments the level set function values by gradient…

The non-monotonic propagation of fronts is considered. When the speed function $F:\mathbb{R}^{n} \times [0,T]\rightarrow \mathbb{R}$ is prescribed, the non-linear advection equation $\phi_{t}+F|\nabla \phi|=0$ is a Hamilton-Jacobi equation…

In this paper we propose a high-order accurate scheme for image segmentation based on the level-set method. In this approach, the curve evolution is described as the 0-level set of a representation function but we modify the velocity that…

Here a semi-implicit formulation of the gradient augmented level set method is presented. By tracking both the level set and it's gradient accurate subgrid information is provided,leading to highly accurate descriptions of a moving…

As one of the most popular interface-capturing methods, the level-set method is inherently non-conservative, and its evolution usually leads to unphysical mass gain/loss. In this paper, a novel conservative level set method is developed for…

We propose a differentiable sphere tracing algorithm to bridge the gap between inverse graphics methods and the recently proposed deep learning based implicit signed distance function. Due to the nature of the implicit function, the…

In spite of its overall efficiency and robustness for capturing the interface in multiphase fluid dynamics simulations, the well-known shortcoming of the level-set method is associated with the lack of a systematic approach for preserving…

For explicit interface tracking in three dimensions, we propose a linear MARS method that (a) represents the interface by a partially ordered set of glued surfaces and approximates each glued surface with a triangular mesh, (b) maintains an…

Accelerated first order methods, also called fast gradient methods, are popular optimization methods in the field of convex optimization. However, they are prone to suffer from oscillatory behaviour that slows their convergence when medium…

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 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…