Iterative Solution of a Retrospective Inverse Heat Conduction Problem with Inhomogeneous Dirichlet Boundary Conditions

被引：0

作者：

Vasil’ev V.I. ^{[1
]}

Kardashevsky A.M. ^{[1
]}

Popov V.V. ^{[1
]}

机构：

[1] North-Eastern Federal University, Yakutsk

来源：

Journal of Applied and Industrial Mathematics | 2022年 / 16卷 / 04期

关键词：

conjugate gradient method; Crank–Nicolson scheme; perturbation condition; retrospective heat conduction problem; Savitzky–Golay filter;

D O I：

10.1134/S1990478922040238

中图分类号：

学科分类号：

摘要：

Abstract: We consider a retrospective inverse heat conduction problem with nonstationaryinhomogeneous Dirichlet boundary conditions. It is approximated by a Crank–Nicolson schemethat has the second order of approximation both in the spatial variable and in time. It is proposedto use the iterative method of conjugate gradients to determine the solution of the resultingsystem of linear algebraic equations. Examples are given of reconstructing smooth, nonsmooth,and discontinuous initial conditions, including the introduction of a “noise” characteristic, typicalof additional conditions of inverse problems, and its smoothing using the Savitzky–Golay filter. © 2022, Pleiades Publishing, Ltd.

引用

页码：841 / 852

页数：11

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