1,720,974 research outputs found
Distributed sampling for rational approximation of the acoustic scattering of an airfoil
No full textIn this paper we compute a reduced order model for a time‐harmonic external acoustic scattering problem with parametric frequency. The employed technique is minimal rational interpolation, an explicit moment‐matching method for Hilbert space‐valued meromorphic maps. We study the approximation and stability properties of this technique for different choices of the sample point set, namely fully distributed in the parameter range, and partially and fully confluent. The proposed technique is also compared with an implicit multi moment‐matching method based on Galerkin projection.CSQISpecial Issue: 90th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM
Interpolatory rational model order reduction of parametric problems lacking uniform inf-sup stability - Numerical tests
No full textCode used to obtain numerical results for Minimal Rational Interpolation of a normal eigenproblem and of a linear elasticity problem in frequency domain.
Associated publication (pre-print available at https://arxiv.org/abs/1905.12954) is under review.</p
RationalROMPy 2.8.3
No full textCopy of the RROMPy library, version 2.8.3. Also available at https://c4science.ch/source/RROMPy/history/master/;2.8.
Interpolatory Rational Model Order Reduction of Parametric Problems Lacking Uniform Inf-Sup Stability
Full text linkWe present a technique for the approximation of a class of Hilbert space--valued maps which arise within the framework of model order reduction (MOR) for parametric partial differential equations, whose solution map has a meromorphic structure. Our MOR strategy consists in constructing an explicit rational approximation based on few snapshots of the solution in an interpolatory fashion. Under some restrictions on the structure of the original problem, we describe a priori convergence results for our technique, hereafter called minimal rational interpolation, which show its ability to identify the main features (e.g., resonance locations) of the target solution map. We also investigate some procedures to obtain a posteriori error indicators, which may be employed to adapt the degree and the sampling points of the minimal rational interpolant. Finally, some numerical experiments are carried out to confirm the theoretical results and the effectiveness of our technique.CSQ
MATHICSE Technical Report: Interpolatory rational model order reduction of parametric problems lacking uniform inf-sup stability
Full text linkWe present a technique for the approximation of a class of Hilbert space-valued maps which arise within the framework of Model Order Reduction for parametric partial differential equations, whose solution map has a meromorphic structure. Our MOR stategy consists in constructing an explicit rational approximation based on few snapshots of the solution, in an interpolatory fashion. Under some restrictions on the structure of the original problem, we describe a priori convergence results for our technique, hereafter called minimal rational interpolation, which show its ability to identify the main features (e.g. resonance locations) of the target solution map. We also investigate some procedures to obtain a posteriori error indicators, which may be employed to adapt the degree and the sampling points of the minimal rational interpolant. Finally, some numerical experiments are carried out to confirm the theoretical results and the effectiveness of our technique.CSQ
Model order reduction based on functional rational approximants for parametric PDEs with meromorphic structure
No full textMany engineering fields rely on frequency-domain dynamical systems for the mathematical modeling of physical (electrical/mechanical/etc.) structures. With the growing need for more accurate and reliable results, the computational burden incurred by frequency sweeps has increased too: in many practical cases, a direct frequency-response analysis over a wide range of frequencies is prohibitively expensive. In this respect, model order reduction (MOR) methods are very appealing, as they allow to replace the costly solves of the original problem with a cheap-to-evaluate surrogate model.
In this work, we describe a MOR approach, dubbed "minimal rational interpolation" (MRI), that builds a rational interpolant of the frequency response of the dynamical system. In MRI, we build a surrogate model in a data-driven fashion, starting from only few (very expensive) solves of the original problem at well-chosen frequencies. Notably, we do not need any knowledge of (nor access to) the underlying structure of the original problem, so that MRI can be described as a "non-intrusive" method. We perform a theoretical analysis of MRI, showing that it converges to the exact frequency response in a quasi-optimal way, in an "approximation theory" sense. We also describe how this approach can be complemented by adaptive sampling strategies, which, relying on a posteriori error estimators, allow to select automatically the "best" sampling frequencies.
Oftentimes, the underlying problem does not depend on frequency alone, but also on additional parameters, which might represent uncertain features of the physical system or design parameters that have to be optimized. This is the so-called "parametric" case, which is much more complex than the non-parametric one, especially if a modest number of parameters is involved. As a way to tackle the parametric setting, we propose a MOR approach based on marginalization: we use MRI to build local frequency surrogates at different parameter configurations, and then we combine these local surrogates to obtain a global reduced model. Several issues arise when carrying our this "combination" step. In this thesis, we propose a practical algorithm for this, relying on matching the partial fraction expansions of the local surrogates term-by-term.
Several numerical experiments are carried out as a way to showcase the effectiveness of our proposed approaches, both in the non-parametric and parametric settings. Our "case studies" are selected as simplified versions of problems of practical interest. Notably, we include examples of resonant behavior of mechanical structures with uncertain material properties, and of impedance modeling of distributed electrical circuits with a modest number of design parameters.CSQ
RationalROMPy 2.2
No full textCopy of the RROMPy library, version 2.2. Also available at https://c4science.ch/source/RROMPy/history/master/;2.
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
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