Multi-material design optimization of optical properties of particulate products by discrete dipole approximation and sequential global programming

The optimal design of nanoparticles with respect to their optical properties is one of the main foci within nanoparticle technology. In this contribution, we suggest a new design optimization method in the framework of which the discrete dipole approximation (DDA) is used to approximate the solution...

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Published in:	Structural and multidisciplinary optimization Vol. 66; no. 1; p. 5
Main Authors:	Nees, Nico, Pflug, Lukas, Mann, Benjamin, Stingl, Michael
Format:	Journal Article
Language:	English
Published:	Berlin/Heidelberg Springer Berlin Heidelberg 01.01.2023 Springer Nature B.V
Subjects:	Algorithms Approximation Computational Mathematics and Numerical Analysis Design optimization Dipoles Engineering Engineering Design Global optimization Material properties Mathematical analysis Mathematical models Nanoparticles Optical properties Research Paper Structural design Theoretical and Applied Mechanics Topology optimization Sequential global programming Discrete dipole approximation Material optimization
ISSN:	1615-147X, 1615-1488
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Abstract	The optimal design of nanoparticles with respect to their optical properties is one of the main foci within nanoparticle technology. In this contribution, we suggest a new design optimization method in the framework of which the discrete dipole approximation (DDA) is used to approximate the solution of Maxwell’s equation in time-harmonic form. In the core of the optimization method, each dipole is repeatedly assigned a material property from a given material catalog until a local minimum for the chosen design objective is obtained. The design updates are computed using a separable model of the optimization objective, which can be solved to global optimality, giving rise to a sequential global optimization (SGP) algorithm. We suggest different types of separable models, among them exact separable models as well as tight approximations of the latter which are numerically tractable. The application of the DDA method in the framework of structural design methods widens the spectrum of numerically tractable layout problems in optical applications as, compared to finite element based approaches, significantly more complex design spaces can be investigated.
AbstractList	The optimal design of nanoparticles with respect to their optical properties is one of the main foci within nanoparticle technology. In this contribution, we suggest a new design optimization method in the framework of which the discrete dipole approximation (DDA) is used to approximate the solution of Maxwell’s equation in time-harmonic form. In the core of the optimization method, each dipole is repeatedly assigned a material property from a given material catalog until a local minimum for the chosen design objective is obtained. The design updates are computed using a separable model of the optimization objective, which can be solved to global optimality, giving rise to a sequential global optimization (SGP) algorithm. We suggest different types of separable models, among them exact separable models as well as tight approximations of the latter which are numerically tractable. The application of the DDA method in the framework of structural design methods widens the spectrum of numerically tractable layout problems in optical applications as, compared to finite element based approaches, significantly more complex design spaces can be investigated.
ArticleNumber	5
Author	Nees, Nico Pflug, Lukas Mann, Benjamin Stingl, Michael
Author_xml	– sequence: 1 givenname: Nico orcidid: 0000-0002-2018-5853 surname: Nees fullname: Nees, Nico email: nico.nees@fau.de organization: Chair of Applied Mathematics (Continuous Optimization), Department of Mathematics, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU) – sequence: 2 givenname: Lukas surname: Pflug fullname: Pflug, Lukas organization: Chair of Applied Mathematics (Continuous Optimization), Department of Mathematics, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Competence Unit for Scientific Computing (CSC), Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU) – sequence: 3 givenname: Benjamin surname: Mann fullname: Mann, Benjamin organization: Competence Unit for Scientific Computing (CSC), Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Chair of Computer Science 10 (System Simulation), Department of Computer Science, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU) – sequence: 4 givenname: Michael surname: Stingl fullname: Stingl, Michael organization: Chair of Applied Mathematics (Continuous Optimization), Department of Mathematics, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Competence Unit for Scientific Computing (CSC), Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU)
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Snippet	The optimal design of nanoparticles with respect to their optical properties is one of the main foci within nanoparticle technology. In this contribution, we...
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SubjectTerms	Algorithms Approximation Computational Mathematics and Numerical Analysis Design optimization Dipoles Engineering Engineering Design Global optimization Material properties Mathematical analysis Mathematical models Nanoparticles Optical properties Research Paper Structural design Theoretical and Applied Mechanics
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Title	Multi-material design optimization of optical properties of particulate products by discrete dipole approximation and sequential global programming
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