By Smelyakov S.V., Stoyan Y.G.
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Additional info for A basis of equivalence classes of paths in optimization problems
Also, there is an increased risk of failure for the optimization algorithm to find a good design (Koziel and Ogurtsov 2012b; see also Chap. 12 for more extensive discussion of this subject). Finer models, on the other hand, are more expensive but they are more likely to produce a useful design with a smaller number of iteration. One can infer from Fig. 4 that the two “finest” coarse-discretization models (with ~400,000 and ~740,000 mesh cells) represent the high-fidelity model response (shown as a thick solid line) quite properly.
Another way of correcting the low-fidelity model is so-called input space mapping (ISM) (Bandler et al. 13) with the model parameters c(i) obtained by minimizing ||Rf(x(i)) − Rc(x(i) + c(i))||. 5 shows an example of a filter structure evaluated using EM simulation (high-fidelity model), its circuit equivalent (low-fidelity model), and the corresponding |S21| responses before and after applying the ISM correction. In many cases, the major type of discrepancy between the low- and high-fidelity models is a frequency shift.
Nowadays, due to the progress in computing hardware as well as development of computational electromagnetic methods, the discrete EM simulators turn to be indispensable for the entire design process starting from a concept estimation step. The use of discrete full-wave simulators is also appealing from the practical point of view and allows obtaining reliable antenna responses with respect to environment and feeds. 48 5 Low-Fidelity Antenna Models Fig. 3 Microstrip antenna (Chen 2008): (a) high-fidelity model shown with a fine tetrahedral mesh and (b) low-fidelity model shown with a much coarser mesh With the discrete solvers, it is the discretization density that has the strongest impact on the accuracy and computational time of a particular antenna model.
A basis of equivalence classes of paths in optimization problems by Smelyakov S.V., Stoyan Y.G.