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首页> 外文期刊>International journal of numerical methods for heat & fluid flow >Determination of volumetric material data from boundary measurements: Revisiting Calderon's problem
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Determination of volumetric material data from boundary measurements: Revisiting Calderon's problem

机译：从边界测量确定体积材料数据：重新审视卡尔德隆的问题

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Purpose - The purpose of this study is to determine the possibility of an accurate assessment of the spatial distribution of material properties such as conductivities or impedances from boundary measurements when the governing partial differential equation is a Laplacian. Design/methodology/approach - A series of numerical experiments were carefully performed. The results were analyzed and compared. Findings - The results to date show that while the optimization procedure is able to obtain spatial distributions of the conductivity k that reduce the cost function significantly, the resulting conductivity k is still significantly different from the target (or real) distribution sought. While the normal fluxes recovered are very close to the prescribed ones, the tangential fluxes can differ considerably. Research limitations/implications - At this point, it is not clear why rigorous mathematical proofs yield results of convergence and uniqueness, while in practice, accurate distributions of the conductivity k seem to be elusive. One possible explanation is that the spatial influence of conductivities decreases exponentially with distance. Thus, many different conductivities inside a domain could give rise to very similar (infinitely close) boundary measurements. Practical implications - This implies that the estimation of field conductivities (or generally field data) from boundary data is far more difficult than previously assumed when the governing partial differential equation in the domain is a Laplacian. This has consequences for material parameter assessments (e.g. for routine maintenance checks of structures), electrical impedance tomography, and many other applications. Originality/value - This is the first time such a finding has been reported in this context.
机译：目的 - 本研究的目的是确定当控制局部微分方程是拉普拉斯时，确定当控制局部微分方程时，可以确定对材料性质的空间分布的可能性，例如来自边界测量的导电性或阻抗。设计/方法/方法 - 仔细进行一系列数值实验。分析并比较结果。结果 - 迄今为止的结果表明，虽然优化程序能够获得显着降低成本函数的电导率K的空间分布，但是导电性k仍然与所寻求的目标（或真实）分布显着不同。虽然回收的正常助熔剂非常接近规定的助熔剂，但切向量可以大大差异。研究限制/影响 - 此时，尚不清楚为什么严格的数学证明会聚和唯一性的结果，而在实践中，电导率K的准确分布似乎是难以捉摸的。一种可能的解释是，电导率的空间影响随着距离指数地减小。因此，域内的许多不同的导电性可能导致非常相似（无限）的边界测量。实际意义 - 这意味着当域中的控制局部微分方程是拉普拉人时，从边界数据估计来自边界数据的场电导率（或通常场数据）的估计远远困难。这对材料参数评估有所后果（例如，用于结构的常规维护检查），电阻断层扫描和许多其他应用。原创/值 - 这是在此背景下报告了这样一个发现的第一次。

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