THE NEED FOR NUMERICAL INTEGRATION (GAUSS QUADRATURE) In my weekly research session tomorrow, I will be talking about numerical integration, Gauss Quadrature in particular, for 2D Finite Element. I will lecture the first half of the session whilst the senior students, Al Akhbar and Mohd Zhafri Jamil will take over the other half to facilitate the programming session since they are well-versed already with the subject matter from their Masters degree training. They will show the juniors how to modify the existing Navier-Stoke derived last week to accommodate this method of integration. But why the need to learn this? You see, in the fluid dynamic source-code they have written last week, the matrices and vectors (e.g K, M, KN etc) were obtained by conducting ANALYTICAL INTEGRATION. However, this was possible only because, all that they have dealt with, were rectangular elements. But in practice, we resort to NUMERICAL INTEGRATION since we are required to deal with irregular element (e.g quadrilateral, curved) so as to have the capability in modeling irregular shape of our problem hence the main advantage of FEM as compared to, say, Finite Difference Method. But why learning it now? Why didnt I teach them from the beginning? Haa you see, I am a true believer to the philosophy that learning must be carried out in an accumulative manner during which, nothing should be left behind, no stone should be left unturned. I maintain to use Analytical Integration until now because it was important for them to get things running first, to get their hand dirty first and get their first result so that they can live what FEM is. But now, since they have finished with this first phase of FEM life, they are in the position to refine their knowledge and skills as we proceed. I always told my students this, have an opinion first on anything, then refine! Speaking of how learning is an accumulative process, tomorrow discussion would also be very important for the immediate future works we are about to undertake as it would be an important pre-requisite to our discussion on Large-Displacement and Arbitrary-Euler-Lagrange. You see, all these aforementioned topics involve the process of mapping from one configuration at one time of interest to another known configuration of a previous time. Such a mapping will require the same forms of Jacobian that would be similar, in a sense, to the one to be found in the discussion of Numerical Integration. Therefore, tomorrow sessions on Numerical Integration will be very important as it can give a sense of familiarity, some convenience feeling and some patterns to trace for immediate future works. So now, my students have all the reasons already to learn about numerical integration and to come to tomorrows research session ;)
Posted on: Sat, 19 Apr 2014 02:41:33 +0000
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