As a follow-up to the discussion here, I am attaching a PUFE homework that I have assigned in 2006 and 2008 when I have offered a meshfree/pufe course. This might be of some help to those who have an interest in partition-of-unity enriched finite element methods.
It has been quite some time (more than 1.5 years) that I had touched upon the topic of the physical bases of FEM in general, and of the general weighted residual (WR) approach in particular, at iMechanica (see here).
The position I then took was that there is no known physical basis at all for the WR approach---despite its loving portrayals in mathematical terms, or its popularity.
Welcome to the February 2009 issue. In this issue, we will discuss the use of finite elements (FEs) in quantum mechanics, with specific focus on the quantum-mechanical problem that arises in crystalline solids. We will consider the electronic structure theory based on the Kohn-Sham equations of density functional theory (KS-DFT): in real-space, Schrödinger and Poisson equations are solved in a parallelepiped unit cell with Bloch-periodic and periodic boundary conditions, respectively.
Based on my limited knowledge of FEM, I find it is difficult to use isoparametric elements for any problem whose governing
functional involve the second (or higher) partial derivatives of the unknown
functions. I hope some computational mechanicians can help me on this. Currently, I have a formulation derived from micropolar elasticity which has a functional involving second partial derivatives of the displacements. Thanks a lot for any of your suggestions.
Dear all,
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GEM Princeton NJ Opportunity -- Senior Research Engineer
Hi, I am a master student in Stuttgart University of Germany
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http://www.msc.commas.uni-stuttgart.de/index.html
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I also have background in Civil Engineering and Computer Science. Please find my CV attached below.
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