Related papers: Constructions of some minimal finite element syste…
In this article, a new generic higher-order finite-element framework for massively parallel simulations is presented. The modular software architecture is carefully designed to exploit the resources of modern and future supercomputers.…
We consider the vanishing ideal of an arrangement of linear subspaces in a vector space and investigate when this ideal can be generated by products of linear forms. We introduce a combinatorial construction (blocker duality) which yields…
We provide a constructive algorithm to find the best separable approximation to an arbitrary density matrix of a composite quantum system of finite dimensions. The method leads to a condition of separability and to a measure of…
This paper addresses problems on the structural design of control systems taking explicitly into consideration the possible application to large-scale systems. We provide an efficient and unified framework to solve the following major…
This paper explores the existence and distribution of primitive elements in finite field extensions with prescribed traces in several intermediate field extensions. Our main result provides an inequality-like condition to ensure the…
The design space for a self-assembled multicomponent objects ranges from a solution in which every building block is unique to one with the minimum number of distinct building blocks that unambiguously define the target structure. Using a…
This paper constructs the first mixed finite element for the linear elasticity problem in 3D using $P_3$ polynomials for the stress and discontinuous $P_2$ polynomials for the displacement on tetrahedral meshes under some mild mesh…
This paper presents a new data-driven finite element framework that is applicable to a broad range of engineering simulation problems. In the data-driven approach, the conservation laws and boundary conditions are satisfied by means of the…
Compatible finite elements provide a framework for preserving important structures in equations of geophysical fluid dynamics, and are becoming important in their use for building atmosphere and ocean models. We survey the application of…
A finite element cochain complex on Cartesian meshes of any dimension based on the H1-inner product is introduced. It yields H1-conforming finite element spaces with exterior derivatives in H1. We use a tensor product construction to obtain…
An introductory theory of frames on finite dimensional quaternion Hilbert spaces is demonstrated along the lines of their complex counterpart.
We compute many dimensions of spaces of finite type invariants of virtual knots (of several kinds) and the dimensions of the corresponding spaces of "weight systems", finding everything to be in agreement with the conjecture that "every…
Composite basis functions for pyramidal elements on the spaces $H^1(\Omega)$, $H(\mathrm{curl},\Omega)$, $H(\mathrm{div},\Omega)$ and $L^2(\Omega)$ are presented. In particular, we construct the lowest-order composite pyramidal elements and…
The Hilbert spaces $H(\mathrm{curl})$ and $H(\mathrm{div})$ are needed for variational problems formulated in the context of the de Rham complex in order to guarantee well-posedness. Consequently, the construction of conforming subspaces is…
The space of elliptic modular forms of fixed weight and level can be identfied with a space of intertwining operators, from a holomorphic discrete series representation of SL2(R) to a space of automorphic forms. Moreover, multiplying…
This paper constructs a unified family of nonconforming finite element spaces for $H\Lambda^k$ in $\mathbb{R}^n$ ($0\leqslant k\leqslant n$, $n\geqslant 1$). The spaces employ piecewise Whitney forms as shape functions, and include the…
By the simple finite element method, we study the symplectic, multisymplectic structures and relevant preserving properties in some semi-linear elliptic boundary value problem in one-dimensional and two-dimensional spaces respectively. We…
The paper deals with a construction of a separating system of rational invariants for finite dimensional generic algebras. In the process of dealing an approach to a rough classification of finite dimensional algebras is offered by…
Finite Element discretizations of coupled multi-physics partial differential equation models require the handling of composed function spaces. In this paper we discuss software concepts and abstractions to handle the composition of function…
We present useful connections between the finite difference and the finite element methods for a model boundary value problem. We start from the observation that, in the finite element context, the interpolant of the solution in one…