Smooth Gradation of Anisotropic Meshes Using Log–Euclidean Metrics

AIAA Journal ◽  
2021 ◽  
pp. 1-18
Author(s):  
Zhoufang Xiao ◽  
Carl Ollivier-Gooch
Keyword(s):  
Anisotropic Meshes ◽  
Euclidean Metrics

NFL Draftnikology: Euclidean Metrics and Other Approaches to Scoring Ranking Predictions

2013 ◽  
Vol 43 (2) ◽  
pp. 237-248
Author(s):  
Steven B. Caudill ◽  
Franklin G. Mixon ◽  
C. Paul Mixon
Keyword(s):  
Euclidean Metrics

scholarly journals The inf-sup stability of the lowest order Taylor–Hood pair on affine anisotropic meshes

2019 ◽  
Vol 40 (4) ◽  
pp. 2377-2398
Author(s):  
Gabriel R Barrenechea ◽  
Andreas Wachtel
Keyword(s):  
Finite Element ◽  
Fluid Mechanics ◽  
Incompressible Fluid ◽  
Stokes Equations ◽  
Sufficient Conditions ◽  
Navier Stokes ◽  
Element Solution ◽  
Navier Stokes Equations ◽  
Anisotropic Meshes ◽  
Theoretical Results

Abstract Uniform inf-sup conditions are of fundamental importance for the finite element solution of problems in incompressible fluid mechanics, such as the Stokes and Navier–Stokes equations. In this work we prove a uniform inf-sup condition for the lowest-order Taylor–Hood pairs $\mathbb{Q}_2\times \mathbb{Q}_1$ and $\mathbb{P}_2\times \mathbb{P}_1$ on a family of affine anisotropic meshes. These meshes may contain refined edge and corner patches. We identify necessary hypotheses for edge patches to allow uniform stability and sufficient conditions for corner patches. For the proof, we generalize Verfürth’s trick and recent results by some of the authors. Numerical evidence confirms the theoretical results.

Convection Problems on Anisotropic Meshes

2013 ◽  
Vol 13 (1) ◽  
pp. 55-78
Author(s):  
Carola Kruse ◽  
Matthias Maischak
Keyword(s):  
Steady State ◽  
Transport Problem ◽  
Annular Domain ◽  
Discontinuous Solutions ◽  
Continuous Solutions ◽  
Edge Singularity ◽  
Unit Square ◽  
Anisotropic Meshes ◽  
Theoretical Part ◽  
Convection Problem

Abstract. The Galerkin and SDFEM methods are compared for a steady state convection problem. The theoretical part of this work deals with the development of approximation results for continuous solutions on the unit square containing an edge singularity. In the numerical part we verify those approximation results by considering continuous as well as discontinuous solutions to the transport problem on an annular domain with a singularity at the inner circle.

Hierarchical elements for the iterative solving of turbulent flow problems on anisotropic meshes

2012 ◽  
Vol 21 (1-2) ◽  
pp. 22-39
Author(s):  
B.A. Wane ◽  
J.M. Urquiza ◽  
A. Fortin ◽  
D. Pelletier
Keyword(s):  
Turbulent Flow ◽  
Flow Problems ◽  
Anisotropic Meshes

Neuroclusterization method of stabilometric data

2021 ◽  
Author(s):  
I.V. Stepanyan ◽  
S.S. Grokhovsky ◽  
O.V. Kubryak
Keyword(s):  
Center Of Pressure ◽  
Modern Method ◽  
Individual Characteristics ◽  
Automatic Mode ◽  
Support Reaction ◽  
Subsequent Determination ◽  
Euclidean Metrics ◽  
Postural Regulation ◽  
The Individual ◽  
Neural Maps

Stabilometry is a modern method for assessing the functional state of a person by the ability to maintain a stable balance of an upright posture. Technically, the implementation of the stabilometry method consists in measuring, with the help of specialized devices, the values that make up the support reaction, with the subsequent determination, according to these measurements, of the coordinates of the center of body pressure on the support. The nature of the migrations of the center of pressure during the stabilometric study is a source of information about the features of the processes of postural regulation. At the same time, up to the present time, there is a problem of the correct interpretation of the results of stabilometry. The adequacy of the conclusions is largely determined by the human factor, i.e. qualification of a specialist analyzing stabilometry data. Thus, in our opinion, the task of objectifying the assessment of stabilometry results is urgent. The aim of this work is to study the possibility of applying the neurocluster method using self-organizing neural networks to objectify the analysis of stabilometry data. The authors proposed a technique for analyzing the structure of individual and group stabilometric data by clustering them using selforganizing Kohonen neural maps with Euclidean metrics. Neuroclusterization of stabilometric data allows in automatic mode (without human intervention) to identify the type of group of subjects corresponding to the norm or pathology, various types of pathologies, as well as individual biometric characteristics of the subjects. The subsequent analysis of the individual characteristics of the data of the subjects, grouped in this way, makes it possible to detect deviations indicating the presence of abnormalities or the formation of various pathological conditions, which can be useful for the early diagnosis of diseases.

scholarly journals Multiple covering of a closed set on a plane with non-Euclidean metrics

2018 ◽  
Vol 51 (32) ◽  
pp. 850-854 ◽  
Author(s):  
Lempert Anna ◽  
Le Quang Mung
Keyword(s):  
Closed Set ◽  
Multiple Covering ◽  
Euclidean Metrics

scholarly journals Geometric Dynamics on Riemannian Manifolds

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 79 ◽  
Author(s):  
Constantin Udriste ◽  
Ionel Tevy
Keyword(s):  
Differential Equations ◽  
Riemannian Manifolds ◽  
Riemannian Metrics ◽  
Second Order ◽  
Time Dynamics ◽  
Outer Planets ◽  
Time Motion ◽  
Euclidean Metrics ◽  
Economical System ◽  
Geometric Dynamics

The purpose of this paper is threefold: (i) to highlight the second order ordinary differential equations (ODEs) as generated by flows and Riemannian metrics (decomposable single-time dynamics); (ii) to analyze the second order partial differential equations (PDEs) as generated by multi-time flows and pairs of Riemannian metrics (decomposable multi-time dynamics); (iii) to emphasise second order PDEs as generated by m-distributions and pairs of Riemannian metrics (decomposable multi-time dynamics). We detail five significant decomposed dynamics: (i) the motion of the four outer planets relative to the sun fixed by a Hamiltonian, (ii) the motion in a closed Newmann economical system fixed by a Hamiltonian, (iii) electromagnetic geometric dynamics, (iv) Bessel motion generated by a flow together with an Euclidean metric (created motion), (v) sinh-Gordon bi-time motion generated by a bi-flow and two Euclidean metrics (created motion). Our analysis is based on some least squares Lagrangians and shows that there are dynamics that can be split into flows and motions transversal to the flows.

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