A heat polynomial method for inverse cylindrical one-phase Stefan problems

IF 1.1 4区工程技术 Q3 ENGINEERING, MULTIDISCIPLINARY

Inverse Problems in Science and Engineering Pub Date : 2021-11-16 DOI:10.1080/17415977.2021.2000977

S. Kassabek, S. Kharin, D. Suragan

引用次数: 4

Abstract

In this paper, solutions of one-phase inverse Stefan problems are studied. The approach presented in the paper is an application of the heat polynomials method (HPM) for solving one- and two-dimensional inverse Stefan problems, where the boundary data is reconstructed on a fixed boundary. We present numerical results illustrating an application of the heat polynomials method for several benchmark examples. We study the effects of accuracy and measurement error for different degree of heat polynomials. Due to ill-conditioning of the matrix generated by HPM, optimization techniques are used to obtain regularized solution. Therefore, the sensitivity of the method to the data disturbance is discussed. Theoretical properties of the proposed method, as well as numerical experiments, demonstrate that to reach accurate results it is quite sufficient to consider only a few of the polynomials. The heat flux for two-dimensional inverse Stefan problem is reconstructed and coefficients of a solution function are found approximately.

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求解反圆柱单相Stefan问题的热多项式方法

本文研究了单相反Stefan问题的解。本文提出的方法是应用热多项式方法（HPM）求解一维和二维反Stefan问题，其中边界数据在固定边界上重建。我们给出了数值结果，说明了热多项式方法在几个基准例子中的应用。我们研究了不同阶热多项式的精度和测量误差的影响。由于HPM生成的矩阵条件不好，因此使用优化技术来获得正则化解。因此，讨论了该方法对数据扰动的敏感性。所提出方法的理论性质以及数值实验表明，为了获得准确的结果，只考虑少数多项式就足够了。重构了二维反Stefan问题的热通量，并近似求出了解函数的系数。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Inverse Problems in Science and Engineering 工程技术-工程：综合

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： Inverse Problems in Science and Engineering provides an international forum for the discussion of conceptual ideas and methods for the practical solution of applied inverse problems. The Journal aims to address the needs of practising engineers, mathematicians and researchers and to serve as a focal point for the quick communication of ideas. Papers must provide several non-trivial examples of practical applications. Multidisciplinary applied papers are particularly welcome. Topics include: -Shape design: determination of shape, size and location of domains (shape identification or optimization in acoustics, aerodynamics, electromagnets, etc; detection of voids and cracks). -Material properties: determination of physical properties of media. -Boundary values/initial values: identification of the proper boundary conditions and/or initial conditions (tomographic problems involving X-rays, ultrasonics, optics, thermal sources etc; determination of thermal, stress/strain, electromagnetic, fluid flow etc. boundary conditions on inaccessible boundaries; determination of initial chemical composition, etc.). -Forces and sources: determination of the unknown external forces or inputs acting on a domain (structural dynamic modification and reconstruction) and internal concentrated and distributed sources/sinks (sources of heat, noise, electromagnetic radiation, etc.). -Governing equations: inference of analytic forms of partial and/or integral equations governing the variation of measured field quantities.