Application of fast automatic differentiation for solving the inverse coefficient problem for the heat equation

被引：10

作者：

Zubov, V. I. ^{[1
,2
]}

机构：

[1] Russian Acad Sci, Dorodnicyn Comp Ctr, Fed Res Ctr Comp Sci & Control, Moscow 119333, Russia

[2] Moscow Inst Phys & Technol, Dolgoprudnyi 141700, Moscow Oblast, Russia

来源：

COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS | 2016年 / 56卷 / 10期

基金：

俄罗斯科学基金会;

关键词：

heat conduction; inverse coefficient problems; gradient; heat equation; adjoint equations; numerical algorithm;

D O I：

10.1134/S0965542516100146

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The problem of determining the thermal conductivity coefficient that depends on temperature is studied. The consideration is based on the initial-boundary value problem for the one-dimensional unsteady heat equation. The mean-root-square deviation of the temperature distribution field and the heat flux from the experimental data on the left boundary of the domain is used as the objective functional. An analytical expression for the gradient of the objective functional is obtained. An algorithm for the numerical solution of the problem based on the modern fast automatic differentiation technique is proposed. Examples of solving the problem are discussed.

引用

页码：1743 / 1757

页数：15

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