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

Utilizing Helicoidal and Translational Symmetries Together in 2-D Models of Twisted Litz Wire Strand Bundles

publishedVersionPeer reviewe

"Pay Now, Argue Later" Rule – Before and After the Tax Administration Act

The South African Revenue Service (SARS) is entrusted with the duty of collecting tax on behalf of the South African government. In order to ensure effective and prompt collection of taxes, the payment of tax is not suspended pending an objection or an appeal, unless directed otherwise. This is also known as the "pay now, argue later" rule, and, for value-added tax purposes, is provided for in terms of section 36 of the Value-Added Tax Act 89 of 1991. The "pay now, argue later" rule in terms of section 36 of the Value-Added Tax Act prima facie infringes on a taxpayer's right of access to the courts as envisaged in section 34 of the Constitution. This is due to the fact that a taxpayer is obliged to pay tax before being afforded the opportunity to challenge the assessment in a court. In Metcash Trading Ltd v Commissioner for the South African Revenue Service, the Constitutional Court held the "pay now, argue later" rule in terms of section 36 to be constitutional. Olivier, however, does not agree with the court on several matters. Amongst the problems she indicates are that the taxpayer does not have access to the courts at the time the rule is invoked, and that the court did not consider the fact that there might be less invasive means available which would ensure that SARS's duty is balanced with the taxpayer's right of access to the courts. Guidelines were also issued which provide legal certainty regarding the factors SARS may consider in determining whether the payment of tax should be suspended or not. These guidelines also evoked some points of criticism. Since 1 October 2012, the "pay now, argue later" rule has been applied in terms of section 164 of the Tax Administration Act 28 of 2011. The question arises whether this provision addresses the problems identified in respect of section 36 of the Value-Added Tax Act and the guidelines. In comparing these sections, only slight differences emerged. The most significant difference is that section 164(6) of the Tax Administration Act stipulates that the enforcement of tax be suspended for a period when SARS is considering a request for suspension. Section 164(6) does not provide a solution to the problems identified regarding section 36 of the Value-Added Tax Act. It is even possible that this section could give rise to further problems. Therefore, the legislature has failed to address the imbalance between the duties of SARS and the right of a taxpayer to access the courts.   

Dimers and the Critical Ising Model on Lattices of genus>1

We study the partition function of both Close-Packed Dimers and the Critical Ising Model on a square lattice embedded on a genus two surface. Using numerical and analytical methods we show that the determinants of the Kasteleyn adjacency matrices have a dependence on the boundary conditions that, for large lattice size, can be expressed in terms of genus two theta functions. The period matrix characterizing the continuum limit of the lattice is computed using a discrete holomorphic structure. These results relate in a direct way the lattice combinatorics with conformal field theory, providing new insight to the lattice regularization of conformal field theories on higher genus Riemann Surfaces.Comment: 44 pages, eps figures included; typos corrected, figure and comments added to section

Modeling Eddy Current Losses in HTS Tapes Using Multiharmonic Method

Due to the highly nonlinear electrical resistivity of high temperature superconducting (HTS) materials, computing the steady-state eddy current losses in HTS tapes, under time-periodic alternating current excitation, can be time consuming when using a time-transient method (TTM). The computation can require several periods to be solved with a small time-step. One alternative to the TTM is the multiharmonic method (MHM) where the Fourier basis is used to approximate the Maxwell fields in time. The method allows obtaining the steady-state solution to the problem with one resolution of the nonlinear problem. In this work, using the finite element method with the H−φ formulation, the capabilities of the MHM in the computational eddy current loss modeling of HTS tapes are scrutinized and compared against the TTM.publishedVersionPeer reviewe

Tapahtuma- ja markkinointisuunnitelma Avoimet ovet -tapahtumaan

Tämän opinnäytetyön tarkoituksena oli luoda tapahtuma- ja markkinointisuunnitelma toimeksiantajayritykselle, urjalalaiselle Hessi-tallille, Avoimet ovet -tapahtumaan. Suunnitelmien pohjalta toteutettiin tapahtuma ja sen markkinointi. Tavoitteena oli suunnitella ja toteuttaa tapahtuma, jonka avulla yritys saa lisää uusia asiakkaita, vahvistaa nykyisiä asiakassuhteita sekä pääsee esittelemään tarjoamiaan palveluita. Tässä toiminnallisessa opinnäytetyössä luotiin tapahtuma- ja markkinointisuunnitelma ja toteutettiin niiden pohjalta Avoimet ovet -tapahtuma. Työssä suunniteltiin myös tapahtuman ja sen markkinoinnin tavoitteet, kohderyhmä, budjetti sekä palautekysely ja toimeksiantajan haastattelu. Palautekyselyn vastausten ja toimeksiantajan haastattelun pohjalta arvioitiin Avoimet ovet -tapahtuman onnistumista ja asetettujen tavoitteiden täyttymistä. Teoriaosuudessa käsiteltiin tapahtuman ja markkinoinnin suunnittelun ja toteutuksen vaiheita, tapahtumamarkkinointia, kohderyhmiä, tavoitteiden asettamista, budjettia sekä palautekyselyn suunnittelua ja toteutusta. Opinnäytetyön toteutuksessa saatiin luotua onnistunut tapahtuma ja sen markkinointi. Tapahtuman tavoitteista budjetin tuottoarvio sekä kävijätavoite toteutuivat erittäin onnistuneesti. Kyselyn perusteella myös itse tapahtuma onnistui todella hyvin ja se koettiin viihdyttäväksi. Lisäksi suurin osa vastaajista kertoi osallistuvansa myös tuleviin Hessi-tallin tapahtumiin. Toimeksiantaja oli myös tyytyväinen tapahtumaan ja koki sen hyödylliseksi yritykselleen. Johtopäätöksiksi saatiin hyviä kehitysideoita tulevia tapahtumia ajatellen

Discretization of Sources of Integral Operators

peer reviewe