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A Unified Approach to Shape and Topological Sensitivity Analysis of Discretized Optimal Design Problems
We introduce a unified sensitivity concept for shape and topological perturbations and perform the sensitivity analysis for a discretized...
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Exploring how ecological and epidemiological processes shape multi-host disease dynamics using global sensitivity analysis
We use global sensitivity analysis (specifically, Partial Rank Correlation Coefficients) to explore the roles of ecological and epidemiological...
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Shape Sensitivity Analysis of a 2D Fluid–Structure Interaction Problem
We study the shape differentiability of a general functional depending on the solution of a bidimensional stationary Stokes–elasticity system with...
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Shape Sensitivity of Eigenvalue Functionals for Scalar Problems: Computing the Semi-derivative of a Minimum
This paper is devoted to the computation of certain directional semi-derivatives of eigenvalue functionals of self-adjoint elliptic operators...
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A Model of Gastric Mucosal pH Regulation: Extending Sensitivity Analysis Using Sobol’ Indices to Understand Higher Moments
Several recent theoretical studies have indicated that a relatively simple secretion control mechanism in the epithelial cells lining the stomach may...
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Boundary shape reconstruction with Robin condition: existence result, stability analysis, and inversion via multiple measurements
This study revisits the problem of identifying the unknown interior Robin boundary of a connected domain using Cauchy data from the exterior region...
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Shape Gradient Methods for Shape Optimization of an Unsteady Multiscale Fluid–Structure Interaction Model
We consider numerical shape optimization of a fluid–structure interaction model. The constrained system involves multiscale coupling of a...
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Bifurcations, chaotic behavior, sensitivity analysis, and various soliton solutions for the extended nonlinear Schrödinger equation
In this manuscript, our primary objective is to delve into the intricacies of an extended nonlinear Schrödinger equation. To achieve this, we...
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Contact Shape Optimization
Contact shape optimization problems in 3D have a structure that can be effectively exploited by the TFETI-based methods introduced in Part III. The...
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Analysis of General Shape Optimization Problems in Nonlinear Acoustics
In various biomedical applications, precise focusing of nonlinear ultrasonic waves is crucial for efficiency and safety of the involved procedures....
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Stability and Sensitivity Analysis for Quasi-Variational Inequalities
We discuss various aspects of quasi-variational inequalities (QVIs) related to their sensitivity analysis and optimal control. Starting with the...
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Modeling, analysis, and simulation of X-shape quasi-zero-stiffness-roller vibration isolators
Existing quasi-zero stiffness (QZS) isolators are reviewed. In terms of their advantages, a novel X-shape QZS isolator combined with the...
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Topological Sensitivity Analysis Method in Identifying of Point Sources via Time-Fractional Diffusion Equation
This work is concerned with an inverse problem for a time-fractional diffusion equation. The aim is to identify point source locations, from a given...
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Geometric Aspects of Shape Optimization
We present a review of known results in shape optimization from the point of view of Geometric Analysis. This paper is devoted to the mathematical...
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Solution of 3D contact shape optimization problems with Coulomb friction based on TFETI
The present paper deals with the numerical solution of 3D shape optimization problems in frictional contact mechanics. Mathematical modelling of the...
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Shape optimization for composite materials in linear elasticity
This article is devoted to the optimal design of the microstructure in composite materials, which are governed by the equations of linear elasticity....
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Recent Development of Medical Shape Analysis via Computational Quasi-conformal Geometry
Medical analysis is closely related to mathematics in many aspects. Over the past decades, mathematicians have designed numerous mathematical models...
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Sensitivity Analysis of a Scalar Mechanical Contact Problem with Perturbation of the Tresca’s Friction Law
This paper investigates the sensitivity analysis of a scalar mechanical contact problem described by a boundary value problem involving the Tresca’s...
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Application of the extended Fourier amplitude sensitivity testing (FAST) method to inflated, axial stretched, and residually stressed cylinders
This paper is dedicated to applying the Fourier amplitude sensitivity test (FAST) method to the problem of mixed extension and inflation of a...
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An efficient 146-line 3D sensitivity analysis code of stress-based topology optimization written in MATLAB
This paper presents an efficient and compact MATLAB code for three-dimensional stress-based sensitivity analysis. The 146 lines code includes the...
