Later, we will show VC-dim(L)=n+1 and VC-dim(F)=n. Note: a few comments about VC-dim and the number of parameters. So far, the examples we give here all satisfy VC-dim=# of parameters. Although that is not always the case, a lot of cases are. ...
When Clough presented the first paper using the finite element terminology in 1960 it attracted the attention of his friend, Professor O. C. Zienkiewicz, who was then on the faculty at Northwestern University. A few weeks after the presentation of the paper Zienkiewicz invited Clough to present ...
Locking phenomena, caused by ill-conditioned global stiffness matrices in finite element analyses, are an often observed and extensively studied issue when modeling nearly incompressible, hyperelastic materials [10,18,46,84,87]. Typically, methods based on Lagrange multipliers are applied to enforce inc...
Go through examples in\exampledirectory. Feedback If you like it, please send me an emaillyc102@gmail.com. If you feel it is helpful for your research, please acknowledge your use by citing: L. Chen. iFEM: an integrated finite element method package in MATLAB. Technical Report, University...
With these three benchmark examples providing confidence that Phreeqc was successfully coupled to a new FE flow and transport framework, the next examples demonstrate the novel and powerful features that this approach provide. Example 4: higher-order DG for reactive transport, convergence analyses, and...
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n}\), and\(D\in {{\mathbb{R}}}^{\ell \times m}\)are known constant matrices that represent the dynamics of the system. We assume that system1is fully controllable and fully observable. In addition,\({\mathcal{U}}\)is a finite set composed ofMvectors, and this set is defined ...
The peaks not identified with this procedure may correspond to trimers and higher order oligomers formed by low molecular weight products, as well as to the products of the reaction pathways not included in the set of ARNG reaction rules, such as the epoxide ring opening reaction. The initial...
Instead of adding into at step 6 in Algorithm 1 , we only add the basis for the corresponding coarse neighborhoods such that is the smallest integer satisfying In the examples below, we will see that the proposed adaptive procedure gives a better convergence and is more efficient. 5. ...
In this section a number of numerical examples obtained with the HOSS software are presented. Generalized Shape Dry Particle InteractionRougier and Munjiza [50] presented a demonstration of FDEM’s capability to model irregular shapes. Unlike with the Discrete Element Method (DEM), the representation...