hp-Finite element discretisation of the electrical impedance tomography problem
hp-Finite element discretisation of the electrical impedance tomography problem
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DOI：
10.1016/j.cma.2012.02.015
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发表时间：
2012-06
影响因子：
7.2
通讯作者：
P. Ledger
中科院分区：
文献类型：
--
作者：
P. Ledger
本文研究了在已知Neumann-Dirichlet映射或Dirichlet-Neumann映射的情况下，从电阻抗层析成像（EIT）逆问题的解中精确恢复介电常数和电导率的问题。线性化的EIT逆问题的傅立叶政权离散的HP-有限元，这使得灵敏度矩阵的条目的准确计算。Knowles（1998）[31]的变分算法被扩展到允许通过在拉普拉斯区域中求解EIT问题来恢复两个材料参数。相关的正问题再次通过hp有限元离散化。一系列的数值结果表明所提出的技术的有效性。
This paper is concerned with the accurate recovery of the permittivity and conductivity from the solution of the electrical impedance tomography (EIT) inverse problem, given the knowledge of either the Neumann to Dirichlet or the Dirichlet to Neumann map. The linearised EIT inverse problem for the Fourier regime is discretised by hp-finite elements, which allows the accurate calculation of the sensitivity matrix entries. The variational algorithm of Knowles (1998) [31] is extended to allow the recovery of both material parameters by solution of the EIT problem in the Laplace regime. The associated forward problem is again discretised by hp-finite elements. A series of numerical results are included to demonstrate the effectiveness of the proposed techniques.