Model order reduction techniques are known to work reliably for finite element-type simulations of micro-electro-mechanical systems devices. These techniques can tremendously shorten computational ...times for transient and harmonic analyses. However, standard model reduction techniques cannot be applied if the equation system incorporates time-varying matrices or parameters that are to be preserved for the reduced model. However, design cycles often involve parameter modification, which should remain possible also in the reduced model. In this article we demonstrate a novel parameterization method to numerically construct highly accurate parametric ordinary differential equation systems based on a small number of systems with different parameter settings. This method is demonstrated to parameterize the geometry of a model of a micro-gyroscope, where the relative error introduced by the parameterization lies in the region of
. We also present recent developments on semi-automatic order reduction methods that can preserve scalar parameters or functions during the reduction process. The first approach is based on a multivariate Padé-type expansion. The second approach is a coupling of the balanced truncation method for model order reduction of (deterministic) linear, time-invariant systems with interpolation. The approach is quite flexible in allowing the use of numerous interpolation techniques like polynomial, Hermite, rational, sinc and spline interpolation. As technical examples we investigate a micro anemometer as well as the gyroscope. Speed-up factors of 20-80 could be achieved, while retaining up to six parameters and keeping typical relative errors below 1%.
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Dostopno za:
DOBA, IZUM, KILJ, NUK, ODKLJ, PILJ, PNG, SAZU, UILJ, UKNU, UL, UM, UPUK
We investigate the numerical solution of large-scale Lyapunov equations with the sign function method. Replacing the usual matrix inversion, addition, and multiplication by formatted arithmetic for ...hierarchical matrices, we obtain an implementation that has linear-polylogarithmic complexity and memory requirements. The method is well suited for Lyapunov operators arising from FEM and BEM approximations to elliptic differential operators. With the sign function method it is possible to obtain a low-rank approximation to a full-rank factor of the solution directly. The task of computing such a factored solution arises, e.g., in model reduction based on balanced truncation. The basis of our method is a partitioned Newton iteration for computing the sign function of a suitable matrix, where one part of the iteration uses formatted arithmetic while the other part directly yields approximations to the full-rank factor of the solution. We discuss some variations of our method and its application to generalized Lyapunov equations. Numerical experiments show that the method can be applied to problems of order up to O(105) on workstations. PUBLICATION ABSTRACT
A 56-year-old woman with unicondylar knee arthroplasty (Oxford III, Biomet) complained of persistent, burning pain in her knee. The arthroplasty failure was caused by a nickel allergy. The diagnosis ...was confirmed by positive patch testing, lymphocyte transformation test and histological analysis of the neosynovia around the implant. The unicondylar knee arthroplasty was explanted and replaced by a titanium-coated knee prosthesis (INNEX CR, Zimmer).
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