Download Scientific Computing in Electrical Engineering 11, 2007-08 by Gabriela Ciuprina, Daniel Ioan (Editors) PDF

By Gabriela Ciuprina, Daniel Ioan (Editors)

This booklet is a suite of chosen papers offered on the final medical Computing in electric Engineering (SCEE) convention, held in Sinaia, Romania, in 2006. The sequence of SCEE meetings goals at addressing mathematical difficulties that have a relevance to undefined, with an emphasis on modeling and numerical simulation of digital circuits, electromagnetic fields but additionally coupled difficulties and common mathematical and computational tools.

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The FE formulation follows from weighting (1) by the test functions wi and integrating by parts. The introduction of the discrete curl operators C and C to the FE grid leads to the same formulation as (5) but with slightly different material matrices and source currents, here indicated by a superscript ·(fe) : M(fe) ν,p,q = νzp · zq dΩ ; (6) σwi · wj dΩ ; (7) (−σ∇φ) · wi dΩ (8) Ω (fe) Mσ,i,j = Ω (fe) j s,i = Ω where Ω denotes the computational domain and zp is the facet element associated with the primary grid facet Sp .

K, are the shifts at iterations j and j + 1 respectively and is the desired convergence tolerance. 4. Project the system matrices Ck = W∗ CV, Gk = W∗ GV, Bk = W∗ B, Lk = LV Upon convergence, the reduced order model satisfies the necessary H2 optimality conditions: ˆ i ), ˆ i ) = Hk (−λ H(−λ d d H(s) |s=−λˆ i = Hk (s) |s=−λˆ i ds ds i = 1, . . , k, ˆ i are the eigenvalues of (Gk , Ck ) (Ritz values). The reduced system therewhere λ fore matches 2k moments of the original at the mirror images of the reduced order poles.

Fig. 2: Hankel singular values, positive real Hankel singular values, eigenvalues of P, eigenvalues of Q. Fig. 2 also shows the trade-off between accuracy and complexity [1]. Choosing a larger order k of the reduced system by truncating the last n−k states gives a smaller approximation error. In particular, for an error of 10%, one needs to keep about half the states, namely 120. We conclude that our circuit is difficult to approximate as the decay of both Lyapunov and Riccati Hankel singular values is slow.

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