Determination of an additive time- and space-dependent coefficient in the heat equation
Determination of an additive time- and space-dependent coefficient in the heat equation
复制标题
热方程中附加时间和空间相关系数的确定
DOI：
10.1108/hff-04-2017-0153
复制
发表时间：
2018
影响因子：
4.2
通讯作者：
T. Johansson
中科院分区：
文献类型：
--
作者：
M. J. Huntul;D. Lesnic;T. Johansson
目的
本研究的目的是提供一个洞察力，并解决数值识别的未知系数的辐射/吸收/灌注出现在热方程从额外的温度测量。
设计/方法/方式
首先，在一种特殊情况下，简要讨论了反系数问题解的唯一性。然而，该问题仍然是不适定的，因为输入数据中的小误差会导致输出解中的大误差。对于数值离散化，使用MATLAB工具箱例程lsqnonlin执行有限差分法结合正则化非线性最小化。
结果
三个例子的数值结果表明，即使在输入数据中存在噪声的计算方法的效率和数值解的准确性和稳定性。
研究限制/影响
数学公式仅限于确定系数，这些系数在单独依赖于时间和空间的未知分量中进行相加分离，这可能被认为是研究的局限性。然而，没有研究意义来克服这一点，因为已知的输入数据也仅限于特定时间和空间位置的温度的单一测量。
实际影响
由于噪声数据被反转，该研究模拟了实际测量固有地被噪声污染的真实的情况。
社会影响
附加的时间和空间依赖的灌注系数的识别将是非常感兴趣的生物传热社区和应用。
独创性/价值
本文的研究是对以往研究的一种改进，即假定低阶温度项的系数分别依赖于时间或空间。在生物医学工程中，了解生物组织中的热传递过程是非常重要的。独创性在于通过第一次进行反演的数值模拟来获得的洞察力，以从嘈杂的测量中找到热方程中与时间和空间相关的系数。
Purpose
The purpose of this study is to provide an insight and to solve numerically the identification of an unknown coefficient of radiation/absorption/perfusion appearing in the heat equation from additional temperature measurements.
Design/methodology/approach
First, the uniqueness of solution of the inverse coefficient problem is briefly discussed in a particular case. However, the problem is still ill-posed as small errors in the input data cause large errors in the output solution. For numerical discretization, the finite difference method combined with a regularized nonlinear minimization is performed using the MATLAB toolbox routine lsqnonlin.
Findings
Numerical results presented for three examples show the efficiency of the computational method and the accuracy and stability of the numerical solution even in the presence of noise in the input data.
Research limitations/implications
The mathematical formulation is restricted to identify coefficients which separate additively in unknown components dependent individually on time and space, and this may be considered as a research limitation. However, there is no research implication to overcome this, as the known input data are also limited to single measurements of temperature at a particular time and space location.
Practical implications
As noisy data are inverted, the study models real situations in which practical measurements are inherently contaminated with noise.
Social implications
The identification of the additive time- and space-dependent perfusion coefficient will be of great interest to the bio-heat transfer community and applications.
Originality/value
The current investigation advances previous studies which assumed that the coefficient multiplying the lower-order temperature term depends on time or space separately. The knowledge of this physical property coefficient is very important in biomedical engineering for understanding the heat transfer in biological tissues. The originality lies in the insight gained by performing for the first time numerical simulations of inversion to find the coefficient additively dependent on time and space in the heat equation from noisy measurements.
影响因子：
2.9
作者：
Fornasier, Massimo;Naumova, Valeriya;Pereverzyev, Sergei V.
通讯作者：
Pereverzyev, Sergei V.