Inverse sensitivity method to self-adjoint systems with repeated eigenvalues

AIAA Journal ◽  
1999 ◽  
Vol 37 ◽  
pp. 933-938
Author(s):  
H. W. Song ◽  
L. F. Chen ◽  
W. L. Wang
Keyword(s):  
Adjoint Systems ◽  
Repeated Eigenvalues ◽  
Sensitivity Method

Inverse Sensitivity Method to Self-Adjoint Systems with Repeated Eigenvalues

AIAA Journal ◽  
10.2514/2.813 ◽  
1999 ◽  
Vol 37 (8) ◽  
pp. 933-938 ◽  
Author(s):  
H. W. Song ◽  
L. F. Chen ◽  
W. L. Wang
Keyword(s):  
Adjoint Systems ◽  
Repeated Eigenvalues ◽  
Sensitivity Method

3-D optimal design of laminated yoke of billet heater for rolling wire rod using ON/OFF method

2012 ◽  
Vol 61 (1) ◽  
pp. 115-123 ◽  
Author(s):  
Norio Takahashi ◽  
Shunsuke Nakazaki ◽  
Daisuke Miyagi ◽  
Naoki Uchida ◽  
Keiji Kawanaka ◽  
...  
Keyword(s):  
Optimal Design ◽  
Local Heating ◽  
Optimization Method ◽  
Optimal Topology ◽  
Field Problem ◽  
Heating Efficiency ◽  
Magnetic Devices ◽  
Wire Rod ◽  
Magnetic Recording Heads ◽  
Sensitivity Method

3-D optimal design of laminated yoke of billet heater for rolling wire rod using ON/OFF method The optimization method using the ON/OFF sensitivity analysis has an advantage that an epoch-making construction of magnetic circuit may be obtained. Therefore, it is attractive for designers of magnetic devices. We have already developed the ON/OFF method for the optimization of a static magnetic field problem, and the effectiveness is verified by applying it to the optimization of magnetic recording heads. In this paper, the ON/OFF sensitivity method is extended to the optimization of the eddy current problem using the adjoint variable. The newly developed ON/OFF method is applied to the determination of the optimal topology of the yoke of the billet heater for rolling wire rod. As a result, the optimal shape of yoke, which we could not imagine beforehand can be obtained. It is shown that the local heating of the yoke was reduced without decreasing the heating efficiency.

Inverse sensitivity method for asymmetric multivariable nondefective systems

AIAA Journal ◽  
2001 ◽  
Vol 39 ◽  
pp. 1600-1607
Author(s):  
L. F. Chen ◽  
H. W. Song ◽  
W. L. Wang
Keyword(s):  
Sensitivity Method

Asymptotic behavior of repeated eigenvalues of perturbed self-adjoint elliptic operators

2021 ◽  
pp. 1-16
Author(s):  
Alexander Dabrowski
Keyword(s):  
General Type ◽  
Differential Operators ◽  
Laplacian Operator ◽  
Variational Characterization ◽  
Repeated Eigenvalues ◽  
Direct Extension ◽  
Asymptotic Formulae ◽  
Elliptic Differential Operators ◽  
Domain Perturbations ◽  
Boundary Deformation

A variational characterization for the shift of eigenvalues caused by a general type of perturbation is derived for second order self-adjoint elliptic differential operators. This result allows the direct extension of asymptotic formulae from simple eigenvalues to repeated ones. Some examples of particular interest are presented theoretically and numerically for the Laplacian operator for the following domain perturbations: excision of a small hole, local change of conductivity, small boundary deformation.

scholarly journals Application of the topological sensitivity method to the reconstruction of plasma equilibrium domain in a tokamak

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Mohamed Abdelwahed ◽  
Nejmeddine Chorfi ◽  
Maatoug Hassine ◽  
Imen Kallel
Keyword(s):  
Inverse Problem ◽  
Asymptotic Expansion ◽  
Numerical Algorithm ◽  
Shape Function ◽  
Optimization Technique ◽  
Plasma Equilibrium ◽  
Topological Sensitivity ◽  
Sensitivity Method

AbstractThe topological sensitivity method is an optimization technique used in different inverse problem solutions. In this work, we adapt this method to the identification of plasma domain in a Tokamak. An asymptotic expansion of a considered shape function is established and used to solve this inverse problem. Finally, a numerical algorithm is developed and tested in different configurations.

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