scholarly journals A-Posteriori-Steered $p$-Robust Multigrid with Optimal Step-Sizes and Adaptive Number of Smoothing Steps

2021 ◽  
pp. S117-S145
Author(s):  
Ani Miraçi ◽  
Jan Papež ◽  
Martin Vohralík
Keyword(s):  
A Posteriori ◽  
Robust Multigrid

scholarly journals Contractive Local Adaptive Smoothing Based on Dörfler’s Marking in A-Posteriori-Steered p-Robust Multigrid Solvers

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Ani Miraçi ◽  
Jan Papež ◽  
Martin Vohralík
Keyword(s):  
Adaptive Algorithm ◽  
Diffusion Problem ◽  
A Posteriori ◽  
Step Size ◽  
Adaptive Smoothing ◽  
Multigrid Solvers ◽  
Numer Anal ◽  
Estimated Error ◽  
Robust Multigrid ◽  
Existing Result

Abstract In this work, we study a local adaptive smoothing algorithm for a-posteriori-steered p-robust multigrid methods. The solver tackles a linear system which is generated by the discretization of a second-order elliptic diffusion problem using conforming finite elements of polynomial order p ≥ 1 {p\geq 1} . After one V-cycle (“full-smoothing” substep) of the solver of [A. Miraçi, J. Papež, and M. Vohralík, A-posteriori-steered p-robust multigrid with optimal step-sizes and adaptive number of smoothing steps, SIAM J. Sci. Comput. 2021, 10.1137/20M1349503], we dispose of a reliable, efficient, and localized estimation of the algebraic error. We use this existing result to develop our new adaptive algorithm: thanks to the information of the estimator and based on a bulk-chasing criterion, cf. [W. Dörfler, A convergent adaptive algorithm for Poisson’s equation, SIAM J. Numer. Anal. 33 1996, 3, 1106–1124], we mark patches of elements with increased estimated error on all levels. Then, we proceed by a modified and cheaper V-cycle (“adaptive-smoothing” substep), which only applies smoothing in the marked regions. The proposed adaptive multigrid solver picks autonomously and adaptively the optimal step-size per level as in our previous work but also the type of smoothing per level (weighted restricted additive or additive Schwarz) and concentrates smoothing to marked regions with high error. We prove that, under a numerical condition that we verify in the algorithm, each substep (full and adaptive) contracts the error p-robustly, which is confirmed by numerical experiments. Moreover, the proposed algorithm behaves numerically robustly with respect to the number of levels as well as to the diffusion coefficient jump for a uniformly-refined hierarchy of meshes.

Practical Correction of Three Fold Astigmatism in the Philips CM TEM

1996 ◽  
Vol 54 ◽  
pp. 418-419
Author(s):  
Arno J. Bleeker ◽  
Mark H.F. Overwijk ◽  
Max T. Otten
Keyword(s):  
Optical Properties ◽  
Phase Contrast ◽  
The Other ◽  
Objective Lens ◽  
Symmetric Part ◽  
A Posteriori ◽  
Contrast Transfer Function ◽  
High Brightness ◽  
Rotationally Symmetric ◽  
Brightness Field

With the improvement of the optical properties of the modern TEM objective lenses the point resolution is pushed beyond 0.2 nm. The objective lens of the CM300 UltraTwin combines a Cs of 0. 65 mm with a Cc of 1.4 mm. At 300 kV this results in a point resolution of 0.17 nm. Together with a high-brightness field-emission gun with an energy spread of 0.8 eV the information limit is pushed down to 0.1 nm. The rotationally symmetric part of the phase contrast transfer function (pctf), whose first zero at Scherzer focus determines the point resolution, is mainly determined by the Cs and defocus. Apart from the rotationally symmetric part there is also the non-rotationally symmetric part of the pctf. Here the main contributors are not only two-fold astigmatism and beam tilt but also three-fold astigmatism. The two-fold astigmatism together with the beam tilt can be corrected in a straight-forward way using the coma-free alignment and the objective stigmator. However, this only works well when the coefficient of three-fold astigmatism is negligible compared to the other aberration coefficients. Unfortunately this is not generally the case with the modern high-resolution objective lenses. Measurements done at a CM300 SuperTwin FEG showed a three fold-astigmatism of 1100 nm which is consistent with measurements done by others. A three-fold astigmatism of 1000 nm already sinificantly influences the image at a spatial frequency corresponding to 0.2 nm which is even above the point resolution of the objective lens. In principle it is possible to correct for the three-fold astigmatism a posteriori when through-focus series are taken or when off-axis holography is employed. This is, however not possible for single images. The only possibility is then to correct for the three-fold astigmatism in the microscope by the addition of a hexapole corrector near the objective lens.

Expected A Posteriori Estimation of Multiple Latent Traits

2005 ◽  
Author(s):  
Damon U. Bryant ◽  
Ashley K. Smith ◽  
Sandra G. Alexander ◽  
Kathlea Vaughn ◽  
Kristophor G. Canali
Keyword(s):  
A Posteriori ◽  
Latent Traits ◽  
Posteriori Estimation

Características Psicométricas de uma Avaliação de Matemática

2020 ◽  
Vol 7 (3) ◽  
pp. 1-27
Author(s):  
Denilson Junio Marques Soares ◽  
Paulo César Emiliano ◽  
Talita Emidio Andrade Soares
Keyword(s):  
A Posteriori

O Departamento de Matemática da Universidade Federal de Viçosa tem realizado algumas medidas de prevenção à reprovação dos estudantes na disciplina de Cálculo, cujos índices têm assustado os professores. Uma dessas medidas está na elaboração de avaliações de matemática básica que objetivam identificar estudantes propensos à reprovação, a fim de proporcionar uma intervenção pedagógica capaz de reverter esta situação. Tendo em vista a importância desta avaliação como parte integrante dos processos de ensino e aprendizagem da disciplina, o presente artigo tem como objetivo oferecer uma análise estatística, pautada nas duas vertentes da Psicometria moderna: a Teoria Clássica dos Testes (TCT) e a Teoria de Resposta ao Item (TRI), e uma análise pedagógica dos descritores e distratores de alguns itens-chave que compõem uma dessas avaliações, escolhida para um estudo de caso. Os resultados apontaram para uma avaliação composta por itens com variados índices de dificuldade e, no geral, com bom poder discriminativo tanto pela análise via TCT, quanto pela TRI, cujos resultados foram obtidos através da estimação, pelo método da média a posteriori, de um modelo logístico de dois parâmetros. A consistência interna da avaliação como instrumento de mensuração de habilidades foi verificada pelo coeficiente alpha de Cronbach, assegurando a qualidade e confiabilidade dos resultados deste estudo. Espera-se que este trabalho sirva como um instrumento de difusão das teorias psicométricas na análise da estrutura de avaliações e aponte para a necessidade de uma maior discussão pedagógica acerca das possíveis lacunas existentes na aprendizagem de matemática básica dos estudantes do ensino superior.

A priori/a posteriori

2017 ◽  
Author(s):  
Heinrich Schepers ◽  
Giorgio Tonelli ◽  
Rudolf Eisler
Keyword(s):  
A Priori ◽  
A Posteriori

Pierre D. Thionet. Quelques problemes concemtlnt les sondages. Goettingen : Vandenhoeck & Ruprecht. 1978. 137pp.

1982 ◽  
Vol 21 (1) ◽  
pp. 83-84
Author(s):  
Karol J. Krotki
Keyword(s):  
Information Theory ◽  
Developing Countries ◽  
Experimental Design ◽  
Bayesian Methods ◽  
English Language ◽  
Applied Statistics ◽  
A Posteriori ◽  
Journal Articles ◽  
Multi Stage ◽  
Theoretical Issues

The publication reviewed is number 9 in the series" Applied Statistics and Econometrics" edited by Gerhard Tintner, Pierre Desire Truonet, and Heinrich Strecker. The purpose of the series is to publish papers " too long for ordinary journal articles, but not long enough for books . ... . . Upon acceptance, speedy publication can be promised". The abstracts in English, French, and German, usual in this series, are missing from the copy reviewed. The book consists of ten chapters: sampling theory; multi -stage sampling and other fundamental problems; optimum stratification; variances; sampling with replacement and other theoretical issues; experimental design; information theory; a posteriori raising factors ; order statistics; Bayesian methods. Such an ambitious content within 130 pages requires parsimonious presentation. One chapter has been squeezed into hardly more than four pages. The chapter on a posteriori raising factors will be useful in developing countries and particularly when samples do not work out as designed. It will also be refreshing to those limited to the literature in the English language.

Comparaison des durées d’incapacité totale de travail attribuées par médecins légistes et urgentistes

2020 ◽  
Author(s):  
L. Fraticelli ◽  
C. Claustre ◽  
L. Boniol ◽  
M. Chambost ◽  
E. Maiello ◽  
...  
Keyword(s):  
Nous Avons ◽  
A Posteriori

Objectif : Comparer les durées d’incapacité totale de travail (ITT) attribuées à la suite d’un passage aux urgences par le médecin urgentiste en charge du patient, et celles attribuées a posteriori par des médecins urgentistes et des médecins légistes. Matériel et méthodes : À partir de l’Observatoire régional des accidents et des traumatismes (ORAT), les accidents de la route et de la vie courante ayant conduit à l’attribution d’une ITT ont été inclus. Trois légistes et trois urgentistes ont attribué a posteriori des durées d’ITT en nombre de jours à partir des informations recueillies dans l’ORAT. La qualité intra- et interprescripteurs a été mesurée. La concordance a été mesurée avec le coefficient de corrélation intraclasse (CCI) et son intervalle de confiance à 95 %. Un accord était observé entre prescripteurs si l’écart entre leurs ITT était inférieur ou égal à 20 % de la moyenne des ITT attribuées. Résultats : La concordance entre légistes était jugée modérée (CCI : 0,67 [0,51 ; 0,80]), de même entre urgentistes (CCI : 0,62 [0,50 ; 0,72]) et entre légistes et urgentistes (CCI : 0,66 [0,59 ; 0,71]). Cependant, seulement 16 % des situations sont en accord. Parmi ces dernières, les patients ne présentaient pas de caractéristiques communes. Ils consultaient généralement le jour même de l’accident et présentaient le plus souvent des lésions à la tête, à la face ou au cou. Parmi les situations de désaccord, les patients présentaient plus fréquemment des lésions à la colonne vertébrale et étaient associés à un handicap n’affectant pas la fonction normale (IIS 1). Conclusion : Nous avons observé une grande hétérogénéité dans l’évaluation entre légistes et urgentistes, qui peut induire une iniquité dans le traitement judiciaire des blessures et dans le suivi médical des victimes.

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