Related papers: A Continuum Theory for Unstructured Mesh Generatio…
A novel approach to unstructured quadrilateral mesh generation for planar domains is presented. Away from irregular vertices, the resulting meshes have the properties of nearly conformal grids. The technique is based on a theoretical…
The presented article contains a 2D mesh generation routine optimized with the Metropolis algorithm. The procedure enables to produce meshes with a prescribed size h of elements. These finite element meshes can serve as standard discrete…
A model describing cell membranes as optimal shapes with regard to the $L^2$-deficit of their mean curvature to a given constant called spontaneous curvature is considered. It is shown that the corresponding energy functional is lower…
We present a method of CutFEM type for the Poisson problem with either Dirichlet or Neumann boundary conditions. The computational mesh is obtained from a background (typically uniform Cartesian) mesh by retaining only the elements…
The paper introduces a Poisson-type problem on a mixed-dimensional structure combining a Euclidean domain and a lower-dimensional self-similar component touching a compact surface (interface). The lower-dimensional piece is a so-called…
One of the major issues in the computational mechanics is to take into account the geometrical complexity. To overcome this difficulty and to avoid the expensive mesh generation, geometrically unfitted methods, i.e. the numerical methods…
This paper introduces a novel method for the efficient second-order accurate computation of normal fields from volume fractions on unstructured polyhedral meshes. Locally, i.e. in each mesh cell, an averaged normal is reconstructed by…
We describe a method for discretizing planar C2-regular domains immersed in non-conforming triangulations. The method consists in constructing mappings from triangles in a background mesh to curvilinear ones that conform exactly to the…
Shape spaces are fundamental in a variety of applications including image registration, morphing, matching, interpolation, and shape optimization. In this work, we consider two-dimensional shapes represented by triangular meshes of a given…
Mapping a shape to some parametric domain is a fundamental tool in graphics and scientific computing. In practice, a map between two shapes is commonly represented by two meshes with same connectivity and different embedding. The standard…
I propound a non-linear generalization of the Poisson equation describing a "medium" in D dimensions with a "dielectric constant" proportional to the field strength to the power D-2. It is the only conformally invariant scalar theory that…
A second-order face-centred finite volume strategy on general meshes is proposed. The method uses a mixed formulation in which a constant approximation of the unknown is computed on the faces of the mesh. Such information is then used to…
In this paper we consider Schwarz domain decomposition applied to the generation of 2D spatial meshes by a local equidistribution principle. We briefly review the derivation of the local equidistribution principle and the appropriate choice…
We prove a structure theorem for the solutions of nonlinear thin two-membrane problems in dimension two. Using the theory of quasi-conformal maps, we show that the difference of the sheets is topologically equivalent to a solution of the…
This paper deals with a simple and straightforward procedure for automatic generation of finite-element or finite-volume meshes of spheroidal domains, consisting of tetrahedra. Besides the equation of the boundary, the generated meshes…
Cell-cell adhesion is an inherently nonlocal phenomenon. Numerous partial differential equation models with nonlocal term have been recently presented to describe this phenomenon, yet the mathematical properties of nonlocal adhesion model…
Projecting fields between different meshes commonly arises in computational physics. This operation requires a supermesh construction and its computational cost is proportional to the number of cells of the supermesh $n$. Given any two…
In this paper, we study the stability of the non symmetric version of the Nitsche's method without penalty for domain decomposition. The Poisson problem is considered as a model problem. The computational domain is divided into two…
We study a coarsening process of one-dimensional cell complexes. We show that if cell boundaries move with velocities proportional to the difference in size of neighboring cells, then the average cell size grows at a prescribed exponential…
We propose conformal generative modeling, a framework for generative modeling on 2D surfaces approximated by discrete triangle meshes. Our approach leverages advances in discrete conformal geometry to develop a map from a source triangle…