Magnetic polarizability tensors (MPTs) provide an economical characterisation of conducting metallic objects and can aid in the solution of metal detection inverse problems, such as scrap metal sorting, searching for unexploded ordnance in areas of former conflict, and security screening at event venues and transport hubs. Previous work has established explicit formulae for their coefficients and a rigorous mathematical theory for the characterisation they provide. In order to assist with efficient computation of MPT spectral signatures of different objects to enable the construction of large dictionaries of characterisations for classification approaches, this work proposes a new, highly-efficient, strategy for predicting MPT coefficients. This is achieved by solving an eddy current type problem using hp-finite elements in combination with a proper orthogonal decomposition reduced order modelling (ROM) methodology and offers considerable computational savings over our previous approach. Furthermore, an adaptive approach is described for generating new frequency snapshots to further improve the accuracy of the ROM. To improve the resolution of highly conducting and magnetic objects, a recipe is proposed to choose the number and thicknesses of prismatic boundary layers for accurate resolution of thin skin depths in such problems. The paper includes a series of challenging examples to demonstrate the success of the proposed methodologies.

翻译：磁极化张量（MPTs）提供了一种经济的导电金属目标表征方法，可辅助解决金属检测逆问题，例如废金属分类、前冲突区域未爆炸物搜寻，以及活动场馆和交通枢纽的安全筛查。前人研究已建立其系数的显式公式，并发展了表征数学理论的严格框架。为高效计算不同目标的MPT谱特征，从而构建用于分类方法的大型表征词典，本文提出了一种新型高效策略来预测MPT系数。该策略通过结合hp有限元与基于本征正交分解的降阶模型（ROM）方法求解涡流问题，相比以往方法大幅降低了计算成本。此外，本文描述了一种自适应方法用于生成新的频率快照，以进一步提升ROM的精度。为改善高导电率与磁性目标的分辨率，本文提出了一种棱柱边界层数量与厚度的选择方案，以精确解析此类问题中的薄趋肤深度。最后通过一系列具有挑战性的算例验证了所提方法的有效性。