Related papers: A C1-mapping based on finite elements on quadrilat…
In this paper, we present a new polygonal finite element method, called the Zipped Finite Element Method, for star-shaped polygons. The proposed approach constructs high-order shape functions as linear combinations of standard finite…
Construction of optimal deformations is one of the long standing problems of computational mathematics. We consider the problem of computing quasi-isometric deformations with minimal possible quasi-isometry constant (global estimate for…
A conforming triangular mixed element recently proposed by Hu and Zhang for linear elasticity is extended by rearranging the global degrees of freedom. More precisely, adaptive meshes $\mathcal{T}_1$, $\cdots$, $\mathcal{T}_N$ which are…
The traditional element-based topology optimization based on material penalization typically aims at a 0/1 design. Our numerical experiments reveal that the compliance of a smooth design is overestimated when material properties of boundary…
A proof of convergence is given for a novel evolving surface finite element semi-discretization of Willmore flow of closed two-dimensional surfaces, and also of surface diffusion flow. The numerical method proposed and studied here…
In the past decade frame fields have emerged as a promising approach for generating hexahedral meshes for CFD and CAE applications. One important problem asks for construction of a boundary-aligned frame field with prescribed singularity…
We develop a family of finite element spaces of differential forms defined on cubical meshes in any number of dimensions. The family contains elements of all polynomial degrees and all form degrees. In two dimensions, these include the…
Despite advances in feature representation, leveraging geometric relations is crucial for establishing reliable visual correspondences under large variations of images. In this work we introduce a Hough transform perspective on…
PETSc's DMPlex interface for unstructured meshes has been extended to support non-conformal meshes. The topological construct that DMPlex implements---the CW-complex---is by definition conformal, so representing non- conformal meshes in a…
Many parametrization and mapping-related problems in geometry processing can be viewed as metric optimization problems, i.e., computing a metric minimizing a functional and satisfying a set of constraints, such as flatness. Penner…
Solving optimization tasks based on functions and losses with a topological flavor is a very active, growing field of research in data science and Topological Data Analysis, with applications in non-convex optimization, statistics and…
Consider discrete conformal maps defined on the basis of two conformally equivalent triangle meshes, that is edge lengths are related by scale factors associated to the vertices. Given a smooth conformal map $f$, we show that it can be…
An algorithm is presented that constructs an acyclic partial matching on the cells of a given simplicial complex from a vector-valued function defined on the vertices and extended to each simplex by taking the least common upper bound of…
An adaptive isogeometric method based on $d$-variate hierarchical spline constructions can be derived by considering a refine module that preserves a certain class of admissibility between two consecutive steps of the adaptive loop [6]. In…
Repetitive patterns are ubiquitous in natural and human-made objects, and can be created with a variety of tools and methods. Manual authoring provides unmatched degree of freedom and control, but can require significant artistic expertise…
In this paper, we present a new numerical method for determining the numerical solution of interface problems to optimal accuracy with respect to the polynomial order of the Lagrangian finite element space on polytopial meshes. We introduce…
Despite the rapidly evolving field of computational electromagnetics, few open-source tools have managed to tackle the problem of automatic mesh generation for properly discretizing the problem of interest into a finite set of elements…
This work concerns adaptive refinement procedures for meshes of polygonal virtual elements. Specifically, refinement procedures previously proposed by the authors for structured meshes are generalized for the challenging case of arbitrary…
Any closed manifold of genus g can be cut open to form a topological disk and then mapped to a regular polygon with 4g sides. This construction is called the canonical polygonal schema of the manifold, and is a key ingredient for many…
We develop primal and mixed variational formulations of transport phenomena on cell complexes with simple polytope connectivity. This framework addresses materials with internal structures comprising components of different topological…