The Experts below are selected from a list of 21954 Experts worldwide ranked by ideXlab platform
Hideyuki Azegami - One of the best experts on this subject based on the ideXlab platform.
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solution of Shape Optimization Problem and its application to product design
2017Co-Authors: Hideyuki AzegamiAbstract:In this paper, we define Shape Optimization Problems as Problems of finding the Shapes of domains in which boundary value Problems of partial differential equations are defined. A domain mapping from an initial domain to a new domain is chosen as the design variable. Functionals of the design variable and the solution to the boundary value Problem are used as cost functions. In this paper, the formulation of the Shape Optimization Problem and a numerical method of solving the Problem are presented. In addition, our subsequent works applying this method to product design are introduced: (1) Shape Optimization of a link mechanism, (2) Shape Optimization for suppressing brake squeal, (3) a method of designing beads in a shell structure, (4) Shape Optimization of a flow field to improve hydrodynamic stability, and (5) Shape Optimization of an electrostatic capacitive sensor.
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Shape Optimization of an electrostatic capacitive sensor
Japan Journal of Industrial and Applied Mathematics, 2016Co-Authors: Masayoshi Satake, Noboru Maeda, Shinji Fukui, Hideyuki AzegamiAbstract:This paper describes the Shape Optimization of an electrostatic capacitive sensor used to detect fingers. We consider two state determination Problems. The first is a basic electrostatic field Problem consisting of sensing electrodes, an earth electrode, and air. The second is an electrostatic field Problem in which fingers are added to the basic electrostatic field Problem. An objective cost function is defined using the negative-signed squared $$H^{1}$$ H 1 -norm of the difference between the solutions of the two state determination Problems. The volume of the sensing electrode is used as the cost function. Using the solutions of the two state determination Problems and the two adjoint Problems, we present a method for evaluating the Shape derivative of the objective cost function. To solve the Shape Optimization Problem and minimize the negative-signed difference norm under the volume constraint, we use an iterative algorithm based on the $$H^{1}$$ H 1 gradient method. An algorithm for the Shape Optimization Problem is developed to solve the boundary value Problems. Numerical examples show that reasonable Shapes are obtained using the present approach.
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Error analysis of the H1 gradient method for Shape-Optimization Problems of continua
JSIAM Letters, 2013Co-Authors: Daisuke Murai, Hideyuki AzegamiAbstract:We present an error estimation for the H1 gradient method, which provides numerical solutions to the Shape-Optimization Problem of the domain in which a boundary value Problem is dened. The main result is that if second-order elements are used for the solutions of the main and adjoint boundary value Problems to evaluate the Shape derivative, and the rstorder elements are used for the solution of domain variation in the boundary value Problem of the H1 gradient method, then we obtain rst-order convergence of the solution of the domain variation with respect to the size of the nite elements.
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Construction method of the cost function for the minimax Shape Optimization Problem
JSIAM Letters, 2013Co-Authors: Kouhei Shintani, Hideyuki AzegamiAbstract:The present paper describes a method by which to formulate a Shape Optimization Problem of a linear elastic continuum for minimizing the maximum value of a strength measure, such as the von Mises stress. In order to avoid the irregularity of the Shape derivative of the maximum value, the Kreisselmeier{St function of the strength measure is used as the cost function. In the cost function, a parameter is used to control the regularity of the Shape derivative. In the present paper, we propose a rule by which to appropriately determine the
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Shape Optimization Problem of elastic bodies for controlling contact pressure
JSIAM Letters, 2010Co-Authors: Takahiro Iwai, Akinobu Sugimoto, Taiki Aoyama, Hideyuki AzegamiAbstract:The present paper describes a numerical solution to Shape Optimization Problems of contacting elastic bodies for controlling contact pressure. The contacting elastic Problem is formulated as the minimization of potential energy with a constraint for penetration based on the large deformation theory. The contact pressure is defined as a Lagrange multiplier for the constraint of penetration in the minimization Problem. An error norm of the contact pressure to a desired distribution is chosen as an objective functional. The Shape derivative of the functional is theoretically evaluated. Numerical solutions are constructed by the traction method.
Bozhidar Velichkov - One of the best experts on this subject based on the ideXlab platform.
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Free boundary regularity for a multiphase Shape Optimization Problem
Communications in Partial Differential Equations, 2019Co-Authors: Luca Spolaor, Baptiste Trey, Bozhidar VelichkovAbstract:AbstractIn this paper we prove a C1,α regularity result in dimension two for almost-minimizers of the constrained one-phase Alt-Caffarelli and the two-phase Alt-Caffarelli-Friedman functionals for ...
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Free boundary regularity for a multiphase Shape Optimization Problem.
arXiv: Analysis of PDEs, 2018Co-Authors: Luca Spolaor, Baptiste Trey, Bozhidar VelichkovAbstract:In this paper we prove a $C^{1,\alpha}$ regularity result in dimension two for almost-minimizers of the constrained one-phase Alt-Caffarelli and the two-phase Alt-Caffarelli-Friedman functionals for an energy with variable coefficients. As a consequence, we deduce the complete regularity of solutions of a multiphase Shape Optimization Problem for the first eigenvalue of the Dirichlet-Laplacian up to the fixed boundary. One of the main ingredient is a new application of the epiperimetric-inequality of Spolaor-Velichkov [CPAM, 2018] up to the boundary. While the framework that leads to this application is valid in every dimension, the epiperimetric inequality is known only in dimension two, thus the restriction on the dimension.
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A Shape Optimal Control Problem with Changing Sign Data
SIAM Journal on Mathematical Analysis, 2018Co-Authors: Giuseppe Buttazzo, Bozhidar VelichkovAbstract:In this paper we consider a Shape Optimization Problem in which the data in the cost functional and in the state equation may change sign, and so no monotonicity assumption is satisfied. Nevertheless, we are able to prove that an optimal domain exists. We also deduce some necessary conditions of optimality for the optimal domain. The results are applied to show the existence of an optimal domain in the case where the cost functional is completely identified, while the right-hand side in the state equation is only known up to a probability P in the space L 2 (D).
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a multiphase Shape Optimization Problem for eigenvalues qualitative study and numerical results
arXiv: Optimization and Control, 2016Co-Authors: Beniamin Bogosel, Bozhidar VelichkovAbstract:We consider the multiphase Shape Optimization Problem $$\min\Big\{\sum_{i=1}^h\lambda_1(\Omega_i)+\alpha|\Omega_i|:\ \Omega_i\ \hbox{open},\ \Omega_i\subset D,\ \Omega_i\cap\Omega_j=\emptyset\Big\},$$ where $\alpha>0$ is a given constant and $ D\subset\Bbb{R}^2$ is a bounded open set with Lipschitz boundary. We give some new results concerning the qualitative properties of the optimal sets and the regularity of the corresponding eigenfunctions. We also provide numerical results for the optimal partitions.
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A Multiphase Shape Optimization Problem for Eigenvalues: Qualitative Study and Numerical Results
SIAM Journal on Numerical Analysis, 2016Co-Authors: Beniamin Bogosel, Bozhidar VelichkovAbstract:In thie paper we consider the following multiphase Shape Optimization Problem $\min\big\{\sum_{i=1}^h\lambda_1(\Omega_i)+\alpha|\Omega_i|:\ \Omega_i\ {open},\ \Omega_i\subset D, \Omega_i\cap\Omega_...
Kathrin Welker - One of the best experts on this subject based on the ideXlab platform.
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computational investigations of an obstacle type Shape Optimization Problem in the space of smooth Shapes
International Conference on Geometric Science of Information, 2019Co-Authors: Daniel Luft, Kathrin WelkerAbstract:We investigate and computationally solve a Shape Optimization Problem constrained by a variational inequality of the first kind, a so-called obstacle-type Problem, with a gradient descent and a BFGS algorithm in the space of smooth Shapes. In order to circumvent the numerical Problems related to the non-linearity of the Shape derivative, we consider a regularization strategy leading to novel possibilities to numerically exploit structures, as well as possible treatment of the regularized variational inequality constrained Shape Optimization in the context of Optimization on infinite dimensional Riemannian manifolds.
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GSI - Computational Investigations of an Obstacle-Type Shape Optimization Problem in the Space of Smooth Shapes
Lecture Notes in Computer Science, 2019Co-Authors: Daniel Luft, Kathrin WelkerAbstract:We investigate and computationally solve a Shape Optimization Problem constrained by a variational inequality of the first kind, a so-called obstacle-type Problem, with a gradient descent and a BFGS algorithm in the space of smooth Shapes. In order to circumvent the numerical Problems related to the non-linearity of the Shape derivative, we consider a regularization strategy leading to novel possibilities to numerically exploit structures, as well as possible treatment of the regularized variational inequality constrained Shape Optimization in the context of Optimization on infinite dimensional Riemannian manifolds.
Daniel Luft - One of the best experts on this subject based on the ideXlab platform.
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computational investigations of an obstacle type Shape Optimization Problem in the space of smooth Shapes
International Conference on Geometric Science of Information, 2019Co-Authors: Daniel Luft, Kathrin WelkerAbstract:We investigate and computationally solve a Shape Optimization Problem constrained by a variational inequality of the first kind, a so-called obstacle-type Problem, with a gradient descent and a BFGS algorithm in the space of smooth Shapes. In order to circumvent the numerical Problems related to the non-linearity of the Shape derivative, we consider a regularization strategy leading to novel possibilities to numerically exploit structures, as well as possible treatment of the regularized variational inequality constrained Shape Optimization in the context of Optimization on infinite dimensional Riemannian manifolds.
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GSI - Computational Investigations of an Obstacle-Type Shape Optimization Problem in the Space of Smooth Shapes
Lecture Notes in Computer Science, 2019Co-Authors: Daniel Luft, Kathrin WelkerAbstract:We investigate and computationally solve a Shape Optimization Problem constrained by a variational inequality of the first kind, a so-called obstacle-type Problem, with a gradient descent and a BFGS algorithm in the space of smooth Shapes. In order to circumvent the numerical Problems related to the non-linearity of the Shape derivative, we consider a regularization strategy leading to novel possibilities to numerically exploit structures, as well as possible treatment of the regularized variational inequality constrained Shape Optimization in the context of Optimization on infinite dimensional Riemannian manifolds.
Beniamin Bogosel - One of the best experts on this subject based on the ideXlab platform.
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regularity result for a Shape Optimization Problem under perimeter constraint
arXiv: Optimization and Control, 2016Co-Authors: Beniamin BogoselAbstract:We study the Problem of optimizing the eigenvalues of the Dirichlet Laplace operator under perimeter constraint. We prove that optimal sets are analytic outside a closed singular set of dimension at most $d-8$ by writing a general optimality condition in the case the optimal eigenvalue is multiple. As a consequence we find that the optimal $k$-th eigenvalue is strictly smaller than the optimal $(k+1)$-th eigenvalue. We also provide an elliptic regularity result for sets with positive and bounded weak curvature.
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a multiphase Shape Optimization Problem for eigenvalues qualitative study and numerical results
arXiv: Optimization and Control, 2016Co-Authors: Beniamin Bogosel, Bozhidar VelichkovAbstract:We consider the multiphase Shape Optimization Problem $$\min\Big\{\sum_{i=1}^h\lambda_1(\Omega_i)+\alpha|\Omega_i|:\ \Omega_i\ \hbox{open},\ \Omega_i\subset D,\ \Omega_i\cap\Omega_j=\emptyset\Big\},$$ where $\alpha>0$ is a given constant and $ D\subset\Bbb{R}^2$ is a bounded open set with Lipschitz boundary. We give some new results concerning the qualitative properties of the optimal sets and the regularity of the corresponding eigenfunctions. We also provide numerical results for the optimal partitions.
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A Multiphase Shape Optimization Problem for Eigenvalues: Qualitative Study and Numerical Results
SIAM Journal on Numerical Analysis, 2016Co-Authors: Beniamin Bogosel, Bozhidar VelichkovAbstract:In thie paper we consider the following multiphase Shape Optimization Problem $\min\big\{\sum_{i=1}^h\lambda_1(\Omega_i)+\alpha|\Omega_i|:\ \Omega_i\ {open},\ \Omega_i\subset D, \Omega_i\cap\Omega_...
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A Multiphase Shape Optimization Problem for Eigenvalues: Qualitative Study and Numerical Results
SIAM Journal on Numerical Analysis, 2016Co-Authors: Beniamin Bogosel, Bozhidar VelichkovAbstract:In this paper we consider the following multiphase Shape Optimization Problem $\min\big\{\sum_{i=1}^h\lambda_1(\Omega_i)+\alpha|\Omega_i|:\ \Omega_i\ {open},\ \Omega_i\subset D, \Omega_i\cap\Omega_j=\emptyset\big\}$, where $\alpha>0$ is a given constant and $D\subset\mathbb{R}^2$ is a bounded open set with Lipschitz boundary. We give some new results concerning the qualitative properties of the optimal sets and the regularity of the corresponding eigenfunctions. We also provide numerical results for the optimal partitions.