Related papers: A partially mesh-free scheme for representing anis…
We consider the problem of estimating a spatially varying density function, motivated by problems that arise in large-scale radiological survey and anomaly detection. In this context, the density functions to be estimated are the background…
A surface moving mesh method is presented for general surfaces with or without explicit parameterization. The method can be viewed as a nontrivial extension of the moving mesh partial differential equation method that has been developed for…
The paper is devoted to the numerical solution of elastoplastic constitutive initial value problems. An improved form of the implicit return-mapping scheme for nonsmooth yield surfaces is proposed that systematically builds on a…
This work aims to describe a mathematical model and a numerical method to simulate a thin anisotropic composite membrane moving and deforming in 3D space under a dynamic load of an arbitrary time and space profile. The model and the method…
Structure functions of rough fracture surfaces in isotropic materials exhibit complicated scaling properties due to the broken isotropy in the fracture plane generated by a preferred propagation direction. Decomposing the structure…
We present a new finite volume scheme for anisotropic heterogeneous diffusion problems on unstructured irregular grids, which simultaneously gives an approximation of the solution and of its gradient. In the case of simplicial meshes, the…
Finite difference based micromagnetic simulations are a powerful tool for the computational investigation of magnetic structures. In this paper, we demonstrate how the discretization of continuous micromagnetic equations introduces a…
As the most common representation for 3D shapes, mesh is often stored discretely with arrays of vertices and faces. However, 3D shapes in the real world are presented continuously. In this paper, we propose to learn a continuous…
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…
We propose a method to simultaneously compute scalar basis functions with an associated functional map for a given pair of triangle meshes. Unlike previous techniques that put emphasis on smoothness with respect to the Laplace--Beltrami…
Multiperforated plates exhibit high gradients and a loss of regularity concentrated in a boundary layer for which a direct numerical simulation becomes very expensive. For elliptic equations the solution at some distance of the boundary is…
Numerical solutions to hyperbolic partial differential equations, involving wave propagations in one direction, are subject to several specific errors, such as numerical dispersion, dissipation or aliasing. In multi-dimensions, where the…
When solving partial differential equations using classical schemes such as finite difference or finite volume methods, sufficiently fine meshes and carefully designed schemes are required to achieve high-order accuracy of numerical…
We highlight some recent new delevelopments concerning the sparse representation of possibly high-dimensional functions exhibiting strong anisotropic features and low regularity in isotropic Sobolev or Besov scales. Specifically, we focus…
Anisotropic mesh adaptation has been successfully applied to the numerical solution of partial differential equations but little considered for variational problems. In this paper, we investigate the use of a global hierarchical basis error…
We develop and test high-order methods for integration on surface point clouds. The task of integrating a function on a surface arises in a range of applications in engineering and the sciences, particularly those involving various integral…
We present a method for differentiable rendering of 3D surfaces that supports both explicit and implicit representations, provides derivatives at occlusion boundaries, and is fast and simple to implement. The method first samples the…
Surfaces are typically represented as meshes, which can be extracted from volumetric fields via meshing or optimized directly as surface parameterizations. Volumetric representations occupy 3D space and have a large effective receptive…
The concern of the present work is the introduction of a very efficient Asymptotic Preserving scheme for the resolution of highly anisotropic diffusion equations. The characteristic features of this scheme are the uniform convergence with…
In this paper, we address a way to reduce the total computational cost of meshless approximation by reducing the required stencil size through spatially varying computational node regularity. Rather than covering the entire domain with…