Interactive 3D subdomaining using adaptive FEM based on solutions to the dual problem

2014 ◽  
Author(s):  
Holger Graf ◽  
Mats Larson ◽  
André Stork
Keyword(s):  
Dual Problem ◽  
Adaptive Fem ◽  
Interactive 3D

scholarly journals Optimal Convergence Rates for Goal-Oriented FEM with Quadratic Goal Functional

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Roland Becker ◽  
Michael Innerberger ◽  
Dirk Praetorius
Keyword(s):  
Dual Problem ◽  
Convergence Rates ◽  
Linear Convergence ◽  
Elliptic Pde ◽  
Optimal Convergence ◽  
Optimal Convergence Rates ◽  
Adaptive Fem ◽  
Numer Anal

AbstractWe consider a linear elliptic PDE and a quadratic goal functional. The goal-oriented adaptive FEM algorithm (GOAFEM) solves the primal as well as a dual problem, where the goal functional is always linearized around the discrete primal solution at hand. We show that the marking strategy proposed in [M. Feischl, D. Praetorius and K. G. van der Zee, An abstract analysis of optimal goal-oriented adaptivity, SIAM J. Numer. Anal.54 (2016), 3, 1423–1448] for a linear goal functional is also optimal for quadratic goal functionals, i.e., GOAFEM leads to linear convergence with optimal convergence rates.

Données LiDAR aériennes: pertinence de l'interprétation visuelle pour la foresterie

2017 ◽  
Vol 168 (3) ◽  
pp. 127-133
Author(s):  
Matthew Parkan
Keyword(s):  
Cross Sections ◽  
Forest Edge ◽  
Airborne Lidar ◽  
Visual Interpretation ◽  
Individual Tree ◽  
Small Areas ◽  
Interactive 3D ◽  
The Individual ◽  
Airborne Lidar Data ◽  
Stem Position

Airborne LiDAR data: relevance of visual interpretation for forestry Airborne LiDAR surveys are particularly well adapted to map, study and manage large forest extents. Products derived from this technology are increasingly used by managers to establish a general diagnosis of the condition of forests. Less common is the use of these products to conduct detailed analyses on small areas; for example creating detailed reference maps like inventories or timber marking to support field operations. In this context, the use of direct visual interpretation is interesting, because it is much easier to implement than automatic algorithms and allows a quick and reliable identification of zonal (e.g. forest edge, deciduous/persistent ratio), structural (stratification) and point (e.g. tree/stem position and height) features. This article examines three important points which determine the relevance of visual interpretation: acquisition parameters, interactive representation and identification of forest characteristics. It is shown that the use of thematic color maps within interactive 3D point cloud and/or cross-sections makes it possible to establish (for all strata) detailed and accurate maps of a parcel at the individual tree scale.

Interactive 3D Visualization with Dual Leap Motions

2018 ◽  
Vol 30 (7) ◽  
pp. 1268 ◽  
Author(s):  
Guodao Sun ◽  
Puyong Huang ◽  
Yipeng Liu ◽  
Ronghua Liang
Keyword(s):  
3D Visualization ◽  
Interactive 3D

scholarly journals Interactive 3D volume rendering in biomedical publications

Micron ◽  
2010 ◽  
Vol 41 (7) ◽  
pp. 886.e1-886.e17 ◽  
Author(s):  
Bernhard Ruthensteiner ◽  
Natalie Baeumler ◽  
David G. Barnes
Keyword(s):  
Volume Rendering ◽  
Interactive 3D ◽  
Biomedical Publications ◽  
3D Volume ◽  
3D Volume Rendering

Interactive 3D displays

Displays ◽  
1991 ◽  
Vol 12 (2) ◽  
pp. 110
Author(s):  
Tencor Instruments
Keyword(s):  
3D Displays ◽  
Interactive 3D

scholarly journals Asymptotic Expansions and Strategies in the Online Increasing Subsequence Problem

2021 ◽  
Vol 174 (1) ◽  
Author(s):  
Amirlan Seksenbayev
Keyword(s):  
Dynamic Programming ◽  
Asymptotic Expansions ◽  
Dual Problem ◽  
Infinite Length ◽  
Expected Time ◽  
Selection Strategies ◽  
Dynamic Programming Equation ◽  
Optimal Values ◽  
Design Selection ◽  
Selection Of

AbstractWe study two closely related problems in the online selection of increasing subsequence. In the first problem, introduced by Samuels and Steele (Ann. Probab. 9(6):937–947, 1981), the objective is to maximise the length of a subsequence selected by a nonanticipating strategy from a random sample of given size $n$ n . In the dual problem, recently studied by Arlotto et al. (Random Struct. Algorithms 49:235–252, 2016), the objective is to minimise the expected time needed to choose an increasing subsequence of given length $k$ k from a sequence of infinite length. Developing a method based on the monotonicity of the dynamic programming equation, we derive the two-term asymptotic expansions for the optimal values, with $O(1)$ O ( 1 ) remainder in the first problem and $O(k)$ O ( k ) in the second. Settling a conjecture in Arlotto et al. (Random Struct. Algorithms 52:41–53, 2018), we also design selection strategies to achieve optimality within these bounds, that are, in a sense, best possible.

scholarly journals On the Classical Capacity of General Quantum Gaussian Measurement

Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 377
Author(s):  
Alexander Holevo
Keyword(s):  
Dual Problem ◽  
Measurement Channel ◽  
Gaussian Channel ◽  
Quantum Communications ◽  
Classical Capacity ◽  
Optimal Ensemble ◽  
Accessible Information ◽  
Measurement Channels ◽  
Gaussian Ensemble ◽  
Average State

In this paper, we consider the classical capacity problem for Gaussian measurement channels. We establish Gaussianity of the average state of the optimal ensemble in the general case and discuss the Hypothesis of Gaussian Maximizers concerning the structure of the ensemble. Then, we consider the case of one mode in detail, including the dual problem of accessible information of a Gaussian ensemble. Our findings are relevant to practical situations in quantum communications where the receiver is Gaussian (say, a general-dyne detection) and concatenation of the Gaussian channel and the receiver can be considered as one Gaussian measurement channel. Our efforts in this and preceding papers are then aimed at establishing full Gaussianity of the optimal ensemble (usually taken as an assumption) in such schemes.

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