Topological sensitivity analysis for a three-dimensional parabolic type problem

2020 ◽  
Vol 120 (3-4) ◽  
pp. 249-272
Author(s):  
Emna Ghezaiel ◽  
Mohamed Abdelwahed ◽  
Nejmeddine Chorfi ◽  
Maatoug Hassine
Keyword(s):  
Sensitivity Analysis ◽  
Three Dimensional ◽  
Parabolic Type ◽  
Mathematical Framework ◽  
Arbitrary Form ◽  
Type Problem ◽  
Shape Functions ◽  
Topological Sensitivity ◽  
Application Model ◽  
Topological Asymptotic Expansion

This work focuses on the topological sensitivity analysis of a three-dimensional parabolic type problem. The considered application model is described by the heat equation. We derive a new topological asymptotic expansion valid for various shape functions and geometric perturbations of arbitrary form. The used approach is based on a rigorous mathematical framework describing and analyzing the asymptotic behavior of the perturbed temperature field.

scholarly journals Shape optimization for the Stokes equations using topological sensitivity analysis

2006 ◽  
Vol Volume 5, Special Issue TAM... ◽  
Author(s):  
Hassine Maatoug
Keyword(s):  
Sensitivity Analysis ◽  
Asymptotic Expansion ◽  
Shape Optimization ◽  
Optimization Problem ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Topological Sensitivity ◽  
Outflow Rate ◽  
International Audience ◽  
Small Obstacle

International audience In this paper, we consider a shape optimization problem related to the Stokes equations. The proposed approach is based on a topological sensitivity analysis. It consists in an asymptotic expansion of a cost function with respect to the insertion of a small obstacle in the domain. The theoretical part of this work is discussed in both two and three dimensional cases. In the numerical part, we use this approach to optimize the shape of the tubes that connect the inlet to the outlets of the cavity maximizing the outflow rate. Dans ce papier, on considère un problème d'optimisation de forme lié aux équations de Stokes. On propose une approche basée sur une analyse de sensibilité topologique. On donne un développement asymptotique d'une fonction coût par rapport à la perturbation du domaine par l'insertion d'un petit obstacle. Des résultats théoriques sont donnés en 2 D et 3 D. Dans la partie numérique, on utilise cette approche pour optimiser la forme des tubes liant l'entrée aux sorties d'une cavité

scholarly journals Topological Sensitivity Analysis for the Anisotropic Laplace Problem

2021 ◽  
Vol 19 (6) ◽  
pp. 949-969
Author(s):  
Imen Kallel
Keyword(s):  
Sensitivity Analysis ◽  
Analysis Method ◽  
Reconstruction Problem ◽  
Topological Sensitivity ◽  
Alternative Approach ◽  
Topological Gradient ◽  
Sensitivity Analysis Method ◽  
Boundary Measurements ◽  
Topological Asymptotic Expansion ◽  
Laplace Problem

This paper is concerned with the reconstruction of objects immersed in anisotropic media from boundary measurements. The aim of this paper is to propose an alternative approach based on the Kohn-Vogelius formulation and the topological sensitivity analysis method. The idea is to formulate the reconstruction problem as a topology optimization one minimizing an energy-like function. We derive a topological asymptotic expansion for the anisotropic Laplace operator. The unknown object is reconstructed using level-set curve of the topological gradient. We make finally some numerical examples proving the efficiency and accuracy of the proposed algorithm.

scholarly journals CONCEPTUAL DESIGN FOR ASSEMBLY IN AEROSPACE INDUSTRY: SENSITIVITY ANALYSIS OF MATHEMATICAL FRAMEWORK AND DESIGN PARAMETERS

2021 ◽  
Vol 1 ◽  
pp. 731-740
Author(s):  
Giovanni Formentini ◽  
Claudio Favi ◽  
Claude Cuiller ◽  
Pierre-Eric Dereux ◽  
Francois Bouissiere ◽  
...  
Keyword(s):  
Sensitivity Analysis ◽  
Conceptual Design ◽  
Design Parameters ◽  
Design For Assembly ◽  
Mathematical Framework ◽  
Commercial Aircraft ◽  
System Architectures ◽  
Complex Engineering ◽  
Aircraft System ◽  
Definition Of

AbstractOne of the most challenging activity in the engineering design process is the definition of a framework (model and parameters) for the characterization of specific processes such as installation and assembly. Aircraft system architectures are complex structures used to understand relation among elements (modules) inside an aircraft and its evaluation is one of the first activity since the conceptual design. The assessment of aircraft architectures, from the assembly perspective, requires parameter identification as well as the definition of the overall analysis framework (i.e., mathematical models, equations).The paper aims at the analysis of a mathematical framework (structure, equations and parameters) developed to assess the fit for assembly performances of aircraft system architectures by the mean of sensitivity analysis (One-Factor-At-Time method). The sensitivity analysis was performed on a complex engineering framework, i.e. the Conceptual Design for Assembly (CDfA) methodology, which is characterized by level, domains and attributes (parameters). A commercial aircraft cabin system was used as a case study to understand the use of different mathematical operators as well as the way to cluster attributes.

scholarly journals Bayesian Quickest Detection Problems for Some Diffusion Processes

2013 ◽  
Vol 45 (1) ◽  
pp. 164-185 ◽  
Author(s):  
Pavel V. Gapeev ◽  
Albert N. Shiryaev
Keyword(s):  
Diffusion Processes ◽  
Free Boundary Problems ◽  
Three Dimensional ◽  
Parabolic Type ◽  
Value Functions ◽  
Weighted Likelihood ◽  
Likelihood Ratios ◽  
Boundary Problems ◽  
Detection Delay ◽  
Penalty Costs

We study the Bayesian problems of detecting a change in the drift rate of an observable diffusion process with linear and exponential penalty costs for a detection delay. The optimal times of alarms are found as the first times at which the weighted likelihood ratios hit stochastic boundaries depending on the current observations. The proof is based on the reduction of the initial problems into appropriate three-dimensional optimal stopping problems and the analysis of the associated parabolic-type free-boundary problems. We provide closed-form estimates for the value functions and the boundaries, under certain nontrivial relations between the coefficients of the observable diffusion.

Wormhole solutions in modified f(R,φ,X) gravity

2021 ◽  
Vol 36 (04) ◽  
pp. 2150021
Author(s):  
M. Farasat Shamir ◽  
Adnan Malik ◽  
G. Mustafa
Keyword(s):  
Shape Function ◽  
Scalar Potential ◽  
Three Dimensional ◽  
State Parameter ◽  
Energy Conditions ◽  
Kinetic Term ◽  
Anisotropic Fluid ◽  
Shape Functions ◽  
Current Analysis ◽  
Static Space

This work aims to investigate the wormhole solutions in the background of [Formula: see text] theory of gravity, where [Formula: see text] is Ricci scalar, [Formula: see text] is scalar potential, and [Formula: see text] is the kinetic term. We consider spherically symmetric static space–time for exploring the wormhole geometry with anisotropic fluid. For our current analysis, we consider a particular equation of state parameter to study the behavior of traceless fluid and examine the physical behavior of energy density and pressure components. Furthermore, we also choose a particular shape function and explore the energy conditions. It can be noticed that energy conditions are violated for both shape functions. The violation of energy conditions indicates the existence of exotic matter and wormhole. Therefore, it can be concluded that our results are stable and realistic. The interesting feature of this work is to show two- and three-dimensional plotting for the analysis of wormhole geometry.

scholarly journals Sensitivity analysis of a coupled hydrodynamic-vegetation model using the effectively subsampled quadratures method (ESQM v5.2)

2017 ◽  
Vol 10 (12) ◽  
pp. 4511-4523 ◽  
Author(s):  
Tarandeep S. Kalra ◽  
Alfredo Aretxabaleta ◽  
Pranay Seshadri ◽  
Neil K. Ganju ◽  
Alexis Beudin
Keyword(s):  
Sensitivity Analysis ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Aquatic Vegetation ◽  
Three Dimensional ◽  
Sensitivity Analyses ◽  
Stem Density ◽  
Sobol Indices ◽  
Plant Stem ◽  
Wave Induced

Abstract. Coastal hydrodynamics can be greatly affected by the presence of submerged aquatic vegetation. The effect of vegetation has been incorporated into the Coupled Ocean–Atmosphere–Wave–Sediment Transport (COAWST) modeling system. The vegetation implementation includes the plant-induced three-dimensional drag, in-canopy wave-induced streaming, and the production of turbulent kinetic energy by the presence of vegetation. In this study, we evaluate the sensitivity of the flow and wave dynamics to vegetation parameters using Sobol' indices and a least squares polynomial approach referred to as the Effective Quadratures method. This method reduces the number of simulations needed for evaluating Sobol' indices and provides a robust, practical, and efficient approach for the parameter sensitivity analysis. The evaluation of Sobol' indices shows that kinetic energy, turbulent kinetic energy, and water level changes are affected by plant stem density, height, and, to a lesser degree, diameter. Wave dissipation is mostly dependent on the variation in plant stem density. Performing sensitivity analyses for the vegetation module in COAWST provides guidance to optimize efforts and reduce exploration of parameter space for future observational and modeling work.

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