THREE-DIMENSIONAL NUMERICAL LOCALIZATION OF IMPERFECTIONS BASED ON A LIMIT MODEL IN ELECTRIC FIELD AND A LIMIT PERTURBATION MODEL

• 来源期刊: 计算数学（英文版）
• 关键词: Inverse problems Maxwell equations Electric fields Inhomogeneities Elec-trical Impedance Tomography Current Projection method FFT Numerical boundary measurements Edge elements Least square systems Incomplete Modified Gram-Schmidt preconditioning
• 年，卷（期）: 2009,（4）
• 页码范围: 495-524
• 页数: 30页
• 语种: 英文
• DOI: 10.4208/jcm.2009.27.4.016

摘要

From a limit model in electric field obtained by letting the frequency vanish in the time-harmonic Maxwell equations, we consider a limit perturbation model in the tangential boundary trace of the curl of the electric field for localizing numerically certain small electromagnetic inhomogeneities, in a three-dimensional bounded domain. We introduce here two localization procedures resulting from the combination of this limit perturbation model with each of the following inversion processes: the Current Projection method and an Inverse Fourier method. Each localization procedure uses, as data, a finite number of boundary measurements, and is employed in the single inhomogeneity case; only the one based on an Inverse Fourier method is required in the multiple inhomogeneities case. Our localization approach is numerically suitable for the context of inhomogeneities that are not purely e|ectric. We compare the numerical results obtained from the two localization procedures in the single inhomogeneity configuration, and describe, in various settings of multiple inhomogeneities, the results provided by the procedure based on an Inverse Fourier method.