Jekyll2022-10-18T09:34:51+00:00https://pabrod.github.io/analytics/feed.xmlElectronic announcement boardPablo Rodríguez-Sánchez2022-10-24T00:00:00+00:002022-10-24T00:00:00+00:00https://pabrod.github.io/analytics/2022/10/24/structure-preserving<p>A talk by <a href="https://www.esciencecenter.nl/team/dr-artur-palha/">dr. Artur Palha</a>.</p> <h2 id="spacetime-coordinates">Spacetime coordinates</h2> <ul> <li>24 October 2022, 11:00 CEST. Location to be announced.</li> </ul> <h2 id="abstract">Abstract</h2> <p>This talk will discuss two fundamental aspects for the construction of structure-preserving discretisations: (i) the definition of the discrete degrees of freedom of physical field quantities (the unknowns), and (ii) the formulation of the physical field laws (the starting point for the discretisation).</p> <p>For the first, geometric degrees of freedom will be introduced. These degrees of freedom are associated to geometric objects (points, lines, surfaces, and volumes), and a relation to differential forms will be remarked. It will be shown that it is possible to construct discrete polynomial function spaces of arbitrary degree associated to these geometric degrees of freedom. Moreover, these function spaces constitute what is called a discrete de Rham complex (spoiler!), mirroring the continuous one.</p> <p>In this way, it is possible to exactly discretise topological equations (to be introduced) even on highly deformed meshes. All approximation errors are included in the constitutive equations (to be introduced). This leads to discretisations that exactly preserve the divergence free constraint of velocity fields in incompressible flow problems and of magnetic fields in electromagnetic problems, for example.</p> <p>For the second, the Navier-Stokes equations will be used as an example and we will show that although at the continuous level all equivalent formulations are equally good, at the discrete level, the choice of a particular formulation has a fundamental impact on the conservation properties of the discretisation.</p> <p>These ideas will be illustrated with the application to the solution of the Poisson equation and Navier-Stokes equations.</p>Artur Palha

A talk by dr. Artur Palha.

2020-10-13T00:00:00+00:002020-10-13T00:00:00+00:00https://pabrod.github.io/analytics/2020/10/13/example<h2 id="spacetime-coordinates">Spacetime coordinates</h2> <ul> <li>13 October 2020, 11:00 CEST. Online, for eScience Center members only.</li> </ul> <h2 id="abstract">Abstract</h2> <p>In this talk you’ll learn how to use this site.</p> <h2 id="links-and-images">Links and images</h2> <p>The slides are temporarily available <a href="https://www.dropbox.com/s/18dmbov56d5vfm2/Complex%20numbers.pptx?dl=0">here</a>.</p> <p><img src="/analytics/assets/img/2020/wing.gif" alt="" /></p> <h2 id="maths">Maths</h2> <!-- Include this script to render mathjax --> <script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js?config=TeX-MML-AM_CHTML" async=""></script> \[e^{i \pi} + 1 = 0\]Pablo Rodríguez-Sánchez

Spacetime coordinates 13 October 2020, 11:00 CEST. Online, for eScience Center members only.