1,720,959 research outputs found
Shape optimization for a noise reduction problem by non-intrusive parametric reduced modeling
No full textWe study a PDE-constrained optimization problem, where the shape and liner material of the nacelle of an aircraft engine are optimized in order to minimize the noise radiated by the engine. More precisely, the acoustic problem is modeled by the Helmholtz equation with varying wavenumber k on an exterior domain. A model reduction strategy is employed to alleviate the cost of the design optimization: the minimal rational interpolation technique is used to construct a surrogate (w.r.t. k) for the quantity of interest at fixed shape/material parameter values, and a parametric model order reduction approach is employed to combine surrogates at different shape/material designs, resulting in a nonintrusive methodology. Numerical experiments for shape and shape/material optimization are provided, to showcase the effectiveness of the presented methodology
Rational-approximation-based model order reduction of Helmholtz frequency response problems with adaptive finite element snapshots
Full text linkWe introduce several spatially adaptive model order reduction approaches tailored to non-coercive elliptic boundary value problems, specifically, parametric-in-frequency Helmholtz problems. The offline information is computed by means of adaptive finite elements, so that each snapshot lives in a different discrete space that resolves the local singularities of the analytical solution and is adjusted to the considered frequency value. A rational surrogate is then assembled adopting either a least-squares or an interpolatory approach, yielding a function-valued version of the the standard rational interpolation method (V-SRI) and the minimal rational interpolation method (MRI). In the context of building an approximation for linear or quadratic functionals of the Helmholtz solution, we perform several numerical experiments to compare the proposed methodologies. Our simulations show that, for interior resonant problems (whose singularities are encoded by poles on the real axis), the spatially adaptive V-SRI and MRI work comparably well. Instead, when dealing with exterior scattering problems, whose frequency response is mostly smooth, the V-SRI method seems to be the best-performing one
Fast least-squares Padé approximation of problems with normal operators and meromorphic structure
Full text linkIn this work, we consider the approximation of Hilbert space-valued meromorphic functions that arise as solution maps of parametric PDEs whose operator is the shift of an operator with normal and compact resolvent, e.g., the Helmholtz equation. In this restrictive setting, we propose a simplified version of the Least-Squares Pade approximation technique studied in [ESAIM Math. Model. Numer. Anal. 52 (2018), pp. 1261-1284] following [J. Approx. Theory 95 (1998), pp. 203-2124]. In particular, the estimation of the poles of the target function reduces to a low-dimensional eigenproblem for a Gramian matrix, allowing for a robust and efficient numerical implementation (hence the "fast" in the name). Moreover, we prove several theoretical results that improve and extend those in [ESAIM Math. Model. Numer. Anal. 52 (2018), pp. 1261-1284], including the exponential decay of the error in the approximation of the poles, and the convergence in measure of the approximant to the target function. The latter result extends the classical one for scalar Pade approximation to our functional framework. We provide numerical results that confirm the improved accuracy of the proposed method with respect to the one introduced in [ESAIM Math. Model. Numer. Anal. 52 (2018), pp. 1261-1284] for differential operators with normal and compact resolvent
Least-Squares Padé approximation of parametric and stochastic Helmholtz maps
Full text linkThe present work deals with rational model order reduction methods based on the single-point Least-Square (LS) Pade approximation techniques introduced in Bonizzoni et al. (ESAIM Math. Model. Numer. Anal., 52(4), 1261-1284 2018, Math. Comput. 89, 1229-1257 2020). Algorithmical aspects concerning the construction of rational LS-Pade approximants are described. In particular, we show that the computation of the Pade denominator can be carried out efficiently by solving an eigenvalue-eigenvector problem involving a Gramian matrix. The LS-Pade techniques are employed to approximate the frequency response map associated with two parametric time-harmonic acoustic wave problems, namely a transmission-reflection problem and a scattering problem. In both cases, we establish the meromorphy of the frequency response map. The Helmholtz equation with stochastic wavenumber is also considered. In particular, for Lipschitz functionals of the solution and their corresponding probability measures, we establish weak convergence of the measure derived from the LS-Pade approximant to the true one. 2D numerical tests are performed, which confirm the effectiveness of the approximation methods
Rational-approximation-based model order reduction of Helmholtz frequency response problems with adaptive finite element snapshots
Full text linkWe introduce several spatially adaptive model order reduction approaches
tailored to non-coercive elliptic boundary value problems, specifically,
parametric-in-frequency Helmholtz problems. The offline information is computed
by means of adaptive finite elements, so that each snapshot lives in a
different discrete space that resolves the local singularities of the
analytical solution and is adjusted to the considered frequency value. A
rational surrogate is then assembled adopting either a least-squares or an
interpolatory approach, yielding function-valued version of the standard
rational interpolation method (-SRI) and the minimal rational
interpolation method (MRI). In the context of building an approximation for
linear or quadratic functionals of the Helmholtz solution, we perform several
numerical experiments to compare the proposed methodologies. Our simulations
show that, for interior resonant problems (whose singularities are encoded by
poles on the real axis), the spatially adaptive -SRI and MRI work
comparably well. Instead, when dealing with exterior scattering problems, whose
frequency response is mostly smooth, the -SRI method seems to be
the best-performing one
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
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Dispelling the Myths Behind First-author Citation Counts
Full text linkWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
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