Geometric Finite Element Discretization of Maxwell Equations in Primal and Dual Spaces

Based on a geometric discretization scheme for Maxwell equations, we unveil a mathematical\textit{\}transformation between the electric field intensity $E$ and the magnetic field intensity $H$, denoted as Galerkin duality. Using Galerkin duality and discrete Hodge operators, we construct two system matrices, $[ X_{E}]$ (primal formulation) and $[ X_{H}$ (dual formulation) respectively, that discretize the second-order vector wave equations. We show that the primal formulation recovers the conventional (edge-element) finite element method (FEM) and suggests a geometric foundation for it. On the other hand, the dual formulation suggests a new (dual) type of FEM. Although both formulations give identical dynamical physical solutions, the dimensions of the null spaces are different.Comment: 22 pages and 4 figure

Complementarity bilateral bounds on forces in magnet systems

It is well known that complementarity can provide bilateral bounds on energy, in numerical approximations of nonlinear magnetostatics. Force is, up to sign, the derivative of energy, so can such bounds also apply to forces, torques, etc.? On the face of it, no, since inequalities are not preserved by differentiation. Yet, useful bounds can be given in some cases, as shown here, following an idea by E. Matagne (Eur. J. Appl. Phys., 25, 107 (2004))

Hierarchic finite element bases on unstructured tetrahedral meshes

The problem of constructing hierarchic bases for finite element discretization of the spaces H1, H(curl), H(div) and L2 on tetrahedral elements is addressed. A simple and efficient approach to ensuring conformity of the approximations across element interfaces is described. Hierarchic bases of arbitrary polynomial order are presented. It is shown how these may be used to construct finite element approximations of arbitrary, non-uniform, local order approximation on unstructured meshes of curvilinear tetrahedral elements

Application of Discrete Differential Forms to Spherically Symmetric Systems in General Relativity

In this article we describe applications of Discrete Differential Forms in computational GR. In particular we consider the initial value problem in vacuum space-times that are spherically symmetric. The motivation to investigate this method is mainly its manifest coordinate independence. Three numerical schemes are introduced, the results of which are compared with the corresponding analytic solutions. The error of two schemes converges quadratically to zero. For one scheme the errors depend strongly on the initial data.Comment: 22 pages, 6 figures, accepted by Class. Quant. Gra

Motion-based technology to support motor skills screening in developing children: A scoping review

Background. Acquiring motor skills is fundamental for children's development since it is linked to cognitive development. However, access to early detection of motor development delays is limited. Aim. This review explores the use and potential of motion-based technology (MBT) as a complement to support and increase access to motor screening in developing children. Methods. Six databases were searched following the PRISMA guidelines to search, select, and assess relevant works where MBT recognised the execution of children's motor skills. Results. 164 studies were analysed to understand the type of MBT used, the motor skills detected, the purpose of using MBT and the age group targeted. Conclusions. There is a gap in the literature aiming to integrate MBT in motor skills development screening and assessment processes. Depth sensors are the prevailing technology offering the largest detection range for children from age 2. Nonetheless, the motor skills detected by MBT represent about half of the motor skills usually observed to screen and assess motor development. Overall, research in this field is underexplored. The use of multimodal approaches, combining various motion-based sensors, may support professionals in the health domain and increase access to early detection programmes.Funding for open access charge: Universidad de Málaga / CBUA

Modelling of periodic electromagnetic structures bianisotropic materials with memory effects

AbstractWe study the behavior of the electromagnetic field of a medium presenting periodic microstructures made of bianisotropic material. We reconsider the classical multi-scale homogenization technique by giving a new approach based upon the periodic unfolding method. The limiting homogeneous constitutive law is thus rigorously justified both in the time domain and in the frequency domain. In particular we show that the limit law differs from the initial one regarding the convolution term accounting for the memory effects

A scoping review and a taxonomy of the use of motion-based technology centered on the end user. A special focus on elderly health

Motion-based technology (MBT) has been applied in the last decades with enormous success in a high number of applications. Its use continues growing and is specially interesting in the health area. Nowadays, its employment is being more and more specialised with respect to the profile of the end user (i.e., child, adolescent/teenager, adult or elderly). This paper first reviews the use of MBT centered in the end user from a global perspective. It also proposes a taxonomy that allows cataloguing the MBT employment directed to the end user. Then, from these results, the paper centers the review on the MBT application aiming to improve the health of elderly. The results highlighted in this paper can help to a better understanding of MBT, especially when it is applied thinking in elderly as the end users.This study is partially funded by the Universidad de Málaga with the national project Bio4Res (PID2021-125184NB-I00) from the Ministerio de Ciencia e Innovaci ́on de Espa ̃na (MCIN). Funding for open access charge: Universidad de Málaga / CBUA

The premetric approach to electromagnetism in the 'waves are not vectors' debate

A plea for the introduction, in advanced electromagnetics courses, of some basic differential geometric notions:  covectors,  differential forms, Hodge operators.  The main advantages of this evolution should be felt in computational electromagnetism.  It may also shed some new light on the concept of material isotropy