Last week I gave a talk at the SCEE conference in Zurich. I’d like to thank the organizers again for giving me the chance to present my work in a 40 minutes keynote talk.
Also, thanks for all the positive feedback and the interesting questions. The slides can be downloaded from here (40 MB).
The animation of the dynamic hp-mesh I showed in the talk can be found here.
Here is an example of a dynamically adapted hp-mesh using SMOVE. I presented the example at the SCEE conference in Sep 2012. The respective slides can be found here.
Press Click To Play and allow for some seconds caching time. If the video doesn’t work (Quicktime plugin required + there appears to be a problem with Firefox) please use one of these direct video links [FLV lo-res (3.4 MB)] [FLV hi-res (14 MB)] [GIF lo-res (3.4 MB)] [GIF hi-res (8.7 MB)].
The top panel shows the y-component of the electric field, below is the estimated element error, next is the adaptation flag (-2: irreducible, -1: reduce, 0: fine, 1: refine, 2: non-refinable) and last is the hp-mesh using embedded triangles for visualizing the tensor product orders (cf. Demkowicz, Solin). The adaptation strategy is HP_ANISO, i.e., allowing for anisotropic refinement in the mesh step size and the polynomial order. The computation and adaptation is done in a three-dimensional domain, the visualizations show cut views.
After finding the initial mesh the mesh step sizes, h, and elementwise approximation orders, p, are adapted autonomously such that the prescribed error tolerance of 1E-5 is met throughout the time-domain simulation (see below or page 70 of the talk).
Below you can see an example of how SMOVE automatically finds an hp-adapted initial mesh to given initial conditions (Gaussian profiles along all coordinates in this case). The left panel shows the magnitude of the electric field (please ignore the visualization artifacts occurring sometimes around the border of the field solution). The right panel shows the process of the mesh adaptation using the refinement strategy HP_ANISO, i.e., allowing for anisotropic refinement in the mesh step size h and the polynomial order p. Keep in mind that this example is meant to demonstrate the adaptation process. The final relative L2-error of the field solution reaches below 1E-9, a ludicrously small error. In a real simulation a less refined mesh would suffice. The computation and adaptation is done in a three-dimensional domain, the visualizations show cut views.
Press Click To Play and allow for some seconds caching time. If the video does not start (Quicktime plugin required + there appears to be a problem with Firefox) please use one of these direct video links [FLV lo-res (800 kB)] [FLV hi-res (1.5 MB)] [GIF lo-res (340 kB)] [GIF hi-res (2.2 MB)].
Martin Lilienthal and myself will attend the ESCO conference in Pilsen, Czech Republic, June 25 – 29, 2012, where I organize a mini-symposium.