Piecewise nonlinear materials and Monotonicity Principle

IF 2 2区数学 Q1 MATHEMATICS, APPLIED

Inverse Problems Pub Date : 2024-06-23 DOI:10.1088/1361-6420/ad575c

Antonio Corbo Esposito, Luisa Faella, Vincenzo Mottola, Gianpaolo Piscitelli, Ravi Prakash and Antonello Tamburrino

引用次数: 0

Abstract

This paper deals with the Monotonicity Principle (MP) for nonlinear materials with piecewise growth exponent. The results obtained are relevant because they enable the use of a fast imaging method based on MP, applied to a wide class of problems with two or more materials, at least one of which is nonlinear. The treatment is very general and makes it possible to model a wide range of practical configurations such as superconducting (SC), perfect electrical conducting (PEC) or perfect electrical insulating (PEI) materials. A key role is played by the average Dirichlet-to-Neumann operator, introduced in Corbo Esposito et al (2021 Inverse Problems37 045012), where the MP for a single type of nonlinearity was treated. Realistic numerical examples confirm the theoretical findings.

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片断非线性材料和单调性原理

本文论述了具有片断增长指数的非线性材料的单调性原理（MP）。所获得的结果具有重要意义，因为这些结果使基于 MP 的快速成像方法得以使用，该方法适用于具有两种或两种以上材料（其中至少一种是非线性材料）的各种问题。这种处理方法非常通用，可以模拟各种实际配置，如超导（SC）、完全导电（PEC）或完全电绝缘（PEI）材料。Corbo Esposito 等人（2021 年逆问题 37 045012）引入的平均 Dirichlet 到 Neumann 算子发挥了关键作用，该算子处理了单一类型非线性的 MP。现实的数值例子证实了理论发现。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Inverse Problems 数学-物理：数学物理

CiteScore

4.40

自引率

14.30%

发文量

115

审稿时长

2.3 months

期刊介绍： An interdisciplinary journal combining mathematical and experimental papers on inverse problems with theoretical, numerical and practical approaches to their solution. As well as applied mathematicians, physical scientists and engineers, the readership includes those working in geophysics, radar, optics, biology, acoustics, communication theory, signal processing and imaging, among others. The emphasis is on publishing original contributions to methods of solving mathematical, physical and applied problems. To be publishable in this journal, papers must meet the highest standards of scientific quality, contain significant and original new science and should present substantial advancement in the field. Due to the broad scope of the journal, we require that authors provide sufficient introductory material to appeal to the wide readership and that articles which are not explicitly applied include a discussion of possible applications.