Related papers: Tangential-Normal Decompositions of Finite Element…
Spline functions have long been used in numerically solving differential equations. Recently it revives as isogeometric analysis, which uses NURBS for both parametrization and element functions. In this paper, we introduce some multivariate…
In this paper, we discuss how to efficiently evaluate and assemble general finite element variational forms on H(div) and H(curl). The proposed strategy relies on a decomposition of the element tensor into a precomputable reference tensor…
We develop the theory of mixed finite elements in terms of special inverse systems of complexes of differential forms, defined over cellular complexes. Inclusion of cells corresponds to pullback of forms. The theory covers for instance…
Motivated by problems where the response is needed at select localized regions in a large computational domain, we devise a novel finite element discretization that results in exponential convergence at pre-selected points. The two key…
Most algorithms constructing bases of finite-dimensional vector spaces return basis vectors which, apart from orthogonality, do not show any special properties. While every basis is sufficient to define the vector space, not all bases are…
In a previous paper [1] it was discussed the viability of functional analysis using as a basis a couple of generic functions, and hence vectorial decomposition. Here we complete the paradigm exploiting one of the analysis methodologies…
We propose a generalized finite element method for the strongly damped wave equation with highly varying coefficients. The proposed method is based on the localized orthogonal decomposition introduced and is designed to handle independent…
For the Hodge--Laplace equation in finite element exterior calculus, we introduce several families of discontinuous Galerkin methods in the extended Galerkin framework. For contractible domains, this framework utilizes seven fields and…
We present a Trefftz-type finite element method on meshes consisting of curvilinear polygons. Local basis functions are computed using integral equation techniques that allow for the efficient and accurate evaluation of quantities needed in…
Continuing the investigation started in a previous work, we consider form factors of integrable quantum field theories in finite volume, extending our investigation to matrix elements with disconnected pieces. Numerical verification of our…
We describe how to obtain a global t-structure from a semiorthogonal decomposition with compatible t-structures on every component. This result is used to generalize a well-known theorem of Bondal on full strong exceptional sequences.
A precise domain triangulation is recognized as indispensable for the accurate numerical approximation of differential operators within collocation methods, leading to a substantial reduction in discretization errors. An efficient finite…
One of the key aspects governing the mechanical performance of composite materials is debonding: the local separation of reinforcing constituents from matrix when the interfacial strength is exceeded. In this contribution, two strategies to…
We develop in this work the first polytopal complexes of differential forms. These complexes, inspired by the Discrete De Rham and the Virtual Element approaches, are discrete versions of the de Rham complex of differential forms built on…
The Galerkin difference (GD) basis is a set of continuous, piecewise polynomials defined using a finite difference like grid of degrees of freedom. The one dimensional GD basis functions are naturally extended to multiple dimensions using…
The irrelevant composite operator $T\bar{T}$, constructed from components of the stress-energy tensor, exhibits unique properties in two-dimensional quantum field theories and represents a distinctive form of integrable deformation.…
This article deals with solving partial differential equations with the finite element method on hybrid non-conforming hexahedral-tetrahedral meshes. By non-conforming, we mean that a quadrangular face of a hexahedron can be connected to…
We introduce a canonical form for reduced bases of integral closures of discrete valuation rings, and we describe an algorithm for computing a basis in reduced normal form. This normal form has the same applications as the Hermite normal…
This paper presents an optimum technique based on the least squares method for the derivation of the bubble functions to enrich the standard linear finite elements employed in the formulation of Galerkin weighted-residual statements. The…
In this paper, gradient-based optimization methods are combined with finite-element modeling for improving electric devices. Geometric design parameters are considered by affine decomposition of the geometry or by the design element…