Minimizing the reflection of waves by surface impedance using boundary elements and global optimization
type: Item
instance of: scholarly article
title: Minimizing the reflection of waves by surface impedance using boundary elements and global optimization
zbMATH Open document ID: 0637.73023
DOI: 10.1016/0165-2125(88)90021-2
author: Thomas J. Bridges
author: Goong Chen
author: Jianxin Zhou
published in: Wave Motion
publication date: 1988-01-01T00:00:00Z
review text: In this paper we consider the problem of minimizing the scattered field intensity with respect to the boundary impedance. Usual optimization procedures based on gradient type local minimization algorithms will not be effective for this problem because the scattered field intensity is not a convex function of the impedance, and it has many local extrema. We approach the problem here by first discretizing the Helmholtz partial differential equation using the boundary element method. Then we apply some recently developed global optimization algorithms [e.g. \textit{Q. Zheng}, Numer. Math., Nanking 7, 31-43 (1985; Zbl 0586.65048)] to find approximate distributions of the boundary impedance for particular shapes which minimize the reflected field intensity. The boundary element method effects a reduction of dimensionality resulting in much greater computational efficiency. The global optimization algorithm allows us to pick out nearly global minimum solutions among many local minima. Numerical solutions are represented graphically and discussed. Our results show that a variable boundary impedance is much more effective for minimizing the scattered field than a constant boundary impedance.
Mathematics Subject Classification ID: 74J20
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 76Q05
Mathematics Subject Classification ID: 49K20
Mathematics Subject Classification ID: 65K10
zbMATH DE Number: 4039406
zbMATH Keywords: minimizing the scattered field intensity
zbMATH Keywords: Helmholtz partial differential equation
zbMATH Keywords: boundary element method
zbMATH Keywords: global optimization algorithms
zbMATH Keywords: approximate distributions of the boundary impedance
zbMATH Keywords: shapes which minimize the reflected field intensity
zbMATH Keywords: nearly global minimum solutions
MaRDI profile type: Publication
full work available at URL: 0165-2125(88)90021-2
OpenAlex ID: W2044255203
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description: scientific article; zbMATH DE number 4039406