Related papers: Discrete Hessian complexes in three dimensions
Let $X$ be a reduced complex space of pure dimension. We consider divergent integrals of certain forms on $X$ that are singular along a subvariety defined by the zero set of a holomorphic section of some holomorphic vector bundle $E…
We propose a new algorithm for tensor decomposition, based on Jennrich's algorithm, and apply our new algorithmic ideas to blind deconvolution and Gaussian mixture models. Our first contribution is a simple and efficient algorithm to…
We explore the recently-proposed Virtual Element Method (VEM) for numerical solution of boundary value problems on arbitrary polyhedral meshes. More specifically, we focus on the elasticity equations in three-dimensions and elaborate upon…
Within a framework of noncommutative geometry, we develop an analogue of (pseudo) Riemannian geometry on finite and discrete sets. On a finite set, there is a counterpart of the continuum metric tensor with a simple geometric…
For a prototype quadratic Hamiltonian describing a driven, dissipative system, exact matrix elements of the reduced density matrix are obtained from a generating function in terms of the normal characteristic functions. The approach is…
Three dimensional wormholes are global solutions of Einstein-Hilbert action. These space-times which are quotients of a part of global AdS$_{3}$ have multiple asymptotic regions, each with conformal boundary $S^{1}\times\mathbb{R}$, and…
This work describes and demonstrates the operation of a virtual X-ray algorithm operating on finite-element post-processing results which allows for higher polynomial orders in geometry representation as well as density distribution. A…
We consider the nonconvex optimization problem associated with the decomposition of a real symmetric tensor into a sum of rank-one terms. Use is made of the rich symmetry structure to construct infinite families of critical points…
Periodic solutions of delay equations are usually approximated as continuous piecewise polynomials on meshes adapted to the solutions' profile. In practical computations this affects the regularity of the (coefficients of the) linearized…
Fitted finite element methods are constructed for a singularly perturbed convection-diffusion problem in two space dimensions. Exponential splines as basis functions are combined with Shishkin meshes to obtain a stable parameter-uniform…
In the framework of virtual element discretizazions, we address the problem of imposing non homogeneous Dirichlet boundary conditions in a weak form, both on polygonal/polyhedral domains and on two/three dimensional domains with curved…
Polynomial meshes (called sometimes "norming sets") allow us to estimate the supremum norm of polynomials on a fixed compact set by the norm on its discrete subset. We give a general construction of polynomial weakly admissible meshes on…
In this paper we present a new Eulerian finite element method for the discretization of scalar partial differential equations on evolving surfaces. In this method we use the restriction of standard space-time finite element spaces on a…
Several types of static solutions to Einstein's equations coupled with antisymmetric tensor fields are found in $(2+N+1)$-dimensional spacetime. The solutions describe a product of a three-dimensional radially symmetric spacetime and an…
Experiments have reached a monumental capacity for designing and synthesizing microscopic particles for self-assembly, making it possible to precisely control particle concentrations, shapes, and interactions. However, more physical insight…
In mixed finite element approximations of Hodge Laplace problems associated with the de Rham complex, the exterior derivative operators are computed exactly, so the spatial locality is preserved. However, the numerical approximations of the…
A higher-order accurate finite element method is proposed which uses automatically generated meshes based on implicit level-set data for the description of boundaries and interfaces in two and three dimensions. The method is an alternative…
The Hodge decomposition provides a very powerful mathematical method for the analysis of 2D and 3D vector fields. It states roughly that any vector field can be $L^2$-orthogonally decomposed into a curl-free, divergence-free, and a harmonic…
It is shown that the h-adaptive mixed finite element method for the discretization of eigenvalue clusters of the Laplace operator produces optimal convergence rates in terms of nonlinear approximation classes. The results are valid for the…
Finite element codes typically use data structures that represent unstructured meshes as collections of cells, faces, and edges, each of which require associated coordinate systems. One then needs to store how the coordinate system of each…