A finite element based tool to support the understanding of electromagnetism concepts

A significant pedagogical innovation in teaching and learning Electromagnetics in undergraduate engineering programmes is the resource to simulations, preferably interactive. A classical approach would require a vector calculus background and three-dimensional geometrical resourcefulness, typically not maturated by undergraduate students. On the other hand, interactive simulations are able to support a meaningful visual insight into the fundamental laws and concepts of electromagnetic theory. This work describes an educational tool which relies in an open source graphical user interface to finite element software, able to provide interaction, accuracy and visual interpretations of the Electromagnetics fundamental laws and classical problems, able to hasten the students’ understanding, by lessening the abstract nature of vector fields, level curves and gradient fields. This tool is to be further developed to gather a set of vast examples and typical problems, able to support a web-based training platform.This work has been supported by FCT - Fundação para a Ciência e Tecnologia within the Project Scope: UIDB/05757/2020.info:eu-repo/semantics/publishedVersio

Time-Domain Finite Elements for Virtual Testing of Electromagnetic Compatibility

The paper presents a time-domain finite-element solver developed for simulations related to solving electromagnetic compatibility issues. The software is applied as a module integrated into a computational framework developed within a FP7 European project High Intensity Radiated Field – Synthetic Environment (HIRF SE) able to simulate a large class of problems. In the paper, the mathematical formulation is briefly presented, and special emphasis is put on the user point of view on the simulation tool-chain. The functionality is demonstrated on the computation of shielding effectiveness of two composite materials. Results are validated through experimental measurements and agreement is confirmed by automatic feature selective algorithms

The FEMM Package: A Simple, Fast, and Accurate Open Source Electromagnetic Tool in Science and Engineering

The finite element method (FEM) is one of the most successful computational techniques for obtaining approximate solutions to the partial differential equations that arise in many scientific and engineering applications. Finite Element Method Magnetics (FEMM) is a software package for solving electromagnetic problems using FEM. The program addresses 2D planar and 3D axisymmetric linear and nonlinear harmonic low frequency magnetic and magnetostatic problems and linear electrostatic problems. It is a simple, accurate, and low computational cost open source product, popular in science, engineering, and education. In this paper the main characteristics and functions of the package are presented. In order to demonstrate its use and exhibit the aid it offers in the study of electromagnetics a series of illustrative examples are given. The aim of the paper is to demonstrate the capability of FEMM to meet as a complementary tool the needs of science and technology especially when factors like the economic cost or the software complexity do not allow the use of commercial products

Singular Higher-Order Complete Vector Bases for Finite Methods

This paper presents new singular curl- and divergence- conforming vector bases that incorporate the edge conditions. Singular bases complete to arbitrarily high order are described in a unified and consistent manner for curved triangular and quadrilateral elements. The higher order basis functions are obtained as the product of lowest order functions and Silvester-Lagrange interpolatory polynomials with specially arranged arrays of interpolation points. The completeness properties are discussed and these bases are proved to be fully compatible with the standard, high-order regular vector bases used in adjacent elements. The curl (divergence) conforming singular bases guarantee tangential (normal) continuity along the edges of the elements allowing for the discontinuity of normal (tangential) components, adequate modeling of the curl (divergence), and removal of spurious modes (solutions). These singular high-order bases should provide more accurate and efficient numerical solutions of both surface integral and differential problems. Sample numerical results confirm the faster convergence of these bases on wedge problems

Maximum Gain, Effective Area, and Directivity

Fundamental bounds on antenna gain are found via convex optimization of the current density in a prescribed region. Various constraints are considered, including self-resonance and only partial control of the current distribution. Derived formulas are valid for arbitrarily shaped radiators of a given conductivity. All the optimization tasks are reduced to eigenvalue problems, which are solved efficiently. The second part of the paper deals with superdirectivity and its associated minimal costs in efficiency and Q-factor. The paper is accompanied with a series of examples practically demonstrating the relevance of the theoretical framework and entirely spanning wide range of material parameters and electrical sizes used in antenna technology. Presented results are analyzed from a perspective of effectively radiating modes. In contrast to a common approach utilizing spherical modes, the radiating modes of a given body are directly evaluated and analyzed here. All crucial mathematical steps are reviewed in the appendices, including a series of important subroutines to be considered making it possible to reduce the computational burden associated with the evaluation of electrically large structures and structures of high conductivity.Comment: 12 pages, 15 figures, submitted to TA