相关论文: Topology of Frame Field Design for Hex Meshing

The coframe field model is known as a viable model for gravity. The principle problem is an interpretation of six additionaldegrees of freedom. We construct a general family of connections which includes the connections of Levi-Civita and…

This paper presents a generalization of symplectic geometry to a principal bundle over the configuration space of a classical field. This bundle, the vertically adapted linear frame bundle, is obtained by breaking the symmetry of the full…

Meshing complex engineering domains is a challenging task. Arbitrary polyhedral meshes can provide the much needed flexibility in automated discretization of such domains. The geometric property of the polyhedral meshes such as the…

We study the topology of the boundary manifold of a regular neighborhood of a complex projective hypersurface. We show that, under certain Hodge theoretic conditions, the cohomology ring of the complement of the hypersurface functorially…

The study of Riemann surfaces with parametrized boundary components was initiated in conformal field theory (CFT). Motivated by general principles from Teichmueller theory, and applications to the construction of CFT from vertex operator…

We determine the homological residue fields, in the sense of tensor-triangular geometry, in a series of concrete examples ranging from topological stable homotopy theory to modular representation theory of finite groups.

In density-based topology optimization, design variables associated to the boundaries of the design domain require unique treatment to negate boundary effects arising from the filtering technique. An effective approach to deal with…

Hexahedral (hex) meshing is a long studied topic in geometry processing with many fascinating and challenging associated problems. Hex meshes vary in complexity from structured to unstructured depending on application or domain of interest.…

Level set-based immersed boundary techniques operate on nonconforming meshes while providing a crisp definition of interface and external boundaries. In such techniques, an isocontour of a level set field interpolated from nodal level set…

Topological conformal field theories are defined using only basic results from the theory of quasiconformal mappings.

Complex geometric tasks such as geometric modeling, physical simulation, and texture parametrization often involve the embedding of many complex sub-domains with potentially different dimensions. These tasks often require evolving the…

Wide variety of engineering design tasks can be formulated as constrained optimization problems where the shape and topology of the domain are optimized to reduce costs while satisfying certain constraints. Several mathematical approaches…

Framed combinatorial topology is a novel theory describing combinatorial phenomena arising at the intersection of stratified topology, singularity theory, and higher algebra. The theory synthesizes elements of classical combinatorial…

The Finite Element Method (FEM) is widely used to solve discrete Partial Differential Equations (PDEs) in engineering and graphics applications. The popularity of FEM led to the development of a large family of variants, most of which…

Hexahedral meshes are an ubiquitous domain for the numerical resolution of partial differential equations. Computing a pure hexahedral mesh from an adaptively refined grid is a prominent approach to automatic hexmeshing, and requires the…

We describe the role conformal nets, a mathematical model for conformal field theory, could play in a geometric definition of the generalized cohomology theory TMF of topological modular forms. Inspired by work of Segal and Stolz-Teichner,…

Higher-dimensional orthogonal packing problems have a wide range of practical applications, including packing, cutting, and scheduling. In the context of a branch-and-bound framework for solving these packing problems to optimality, it is…

Some combinatorial properties of fixed boundary rhombus random tilings with octagonal symmetry are studied. A geometrical analysis of their configuration space is given as well as a description in terms of discrete dynamical systems, thus…

If a finite element mesh contains concave elements, it is said to tangled. Tangled meshes can occur during mesh generation, mesh optimization, and large deformation simulations, and will lead to erroneous results during finite element…

Many tasks in geometry processing are modeled as variational problems solved numerically using the finite element method. For solid shapes, this requires a volumetric discretization, such as a boundary conforming tetrahedral mesh.…