Vincenzo Mottola, A. Corbo Esposito, Gianpaolo Piscitelli, A. Tamburrino
{"title":"通过单调性原理对非线性材料进行断层扫描","authors":"Vincenzo Mottola, A. Corbo Esposito, Gianpaolo Piscitelli, A. Tamburrino","doi":"10.3233/jae-230129","DOIUrl":null,"url":null,"abstract":"In this paper we present a first non-iterative imaging method for nonlinear materials, based on Monotonicity Principle. Specifically, we deal with the inverse obstacle problem, where the aim is to retrieve a nonlinear anomaly embedded in linear known background. The Monotonicity Principle (MP) is a general property for various class of PDEs, that has recently generalized to nonlinear elliptic PDEs. Basically, it states a monotone relation between the point-wise value of the unknown material property and the boundary measurements. It is at the foundation of a class of non-iterative imaging methods, characterized by a very low execution time that makes them ideal candidates for real-time applications. In this work, we develop an inversion method that overcomes some of the peculiar difficulties in practical application of MP to imaging of nonlinear materials, preserving the feasibility for real-time applications. For the sake of clarity, we focus on a specific application, i.e. the Magnetostatic Permeability Tomography where the goal is retrieving the unknown (nonlinear) permeability by boundary measurements in DC operations. This choice is motivated by applications in the inspection of boxes and containers for security. Reconstructions from simulated data prove the effectiveness of the presented method.","PeriodicalId":50340,"journal":{"name":"International Journal of Applied Electromagnetics and Mechanics","volume":null,"pages":null},"PeriodicalIF":1.1000,"publicationDate":"2024-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Tomography of nonlinear materials via the monotonicity principle\",\"authors\":\"Vincenzo Mottola, A. Corbo Esposito, Gianpaolo Piscitelli, A. Tamburrino\",\"doi\":\"10.3233/jae-230129\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper we present a first non-iterative imaging method for nonlinear materials, based on Monotonicity Principle. Specifically, we deal with the inverse obstacle problem, where the aim is to retrieve a nonlinear anomaly embedded in linear known background. The Monotonicity Principle (MP) is a general property for various class of PDEs, that has recently generalized to nonlinear elliptic PDEs. Basically, it states a monotone relation between the point-wise value of the unknown material property and the boundary measurements. It is at the foundation of a class of non-iterative imaging methods, characterized by a very low execution time that makes them ideal candidates for real-time applications. In this work, we develop an inversion method that overcomes some of the peculiar difficulties in practical application of MP to imaging of nonlinear materials, preserving the feasibility for real-time applications. For the sake of clarity, we focus on a specific application, i.e. the Magnetostatic Permeability Tomography where the goal is retrieving the unknown (nonlinear) permeability by boundary measurements in DC operations. This choice is motivated by applications in the inspection of boxes and containers for security. Reconstructions from simulated data prove the effectiveness of the presented method.\",\"PeriodicalId\":50340,\"journal\":{\"name\":\"International Journal of Applied Electromagnetics and Mechanics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2024-01-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Applied Electromagnetics and Mechanics\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://doi.org/10.3233/jae-230129\",\"RegionNum\":4,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"ENGINEERING, ELECTRICAL & ELECTRONIC\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Applied Electromagnetics and Mechanics","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.3233/jae-230129","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"ENGINEERING, ELECTRICAL & ELECTRONIC","Score":null,"Total":0}
Tomography of nonlinear materials via the monotonicity principle
In this paper we present a first non-iterative imaging method for nonlinear materials, based on Monotonicity Principle. Specifically, we deal with the inverse obstacle problem, where the aim is to retrieve a nonlinear anomaly embedded in linear known background. The Monotonicity Principle (MP) is a general property for various class of PDEs, that has recently generalized to nonlinear elliptic PDEs. Basically, it states a monotone relation between the point-wise value of the unknown material property and the boundary measurements. It is at the foundation of a class of non-iterative imaging methods, characterized by a very low execution time that makes them ideal candidates for real-time applications. In this work, we develop an inversion method that overcomes some of the peculiar difficulties in practical application of MP to imaging of nonlinear materials, preserving the feasibility for real-time applications. For the sake of clarity, we focus on a specific application, i.e. the Magnetostatic Permeability Tomography where the goal is retrieving the unknown (nonlinear) permeability by boundary measurements in DC operations. This choice is motivated by applications in the inspection of boxes and containers for security. Reconstructions from simulated data prove the effectiveness of the presented method.
期刊介绍:
The aim of the International Journal of Applied Electromagnetics and Mechanics is to contribute to intersciences coupling applied electromagnetics, mechanics and materials. The journal also intends to stimulate the further development of current technology in industry. The main subjects covered by the journal are:
Physics and mechanics of electromagnetic materials and devices
Computational electromagnetics in materials and devices
Applications of electromagnetic fields and materials
The three interrelated key subjects – electromagnetics, mechanics and materials - include the following aspects: electromagnetic NDE, electromagnetic machines and devices, electromagnetic materials and structures, electromagnetic fluids, magnetoelastic effects and magnetosolid mechanics, magnetic levitations, electromagnetic propulsion, bioelectromagnetics, and inverse problems in electromagnetics.
The editorial policy is to combine information and experience from both the latest high technology fields and as well as the well-established technologies within applied electromagnetics.