BEM-Fading regularization algorithm for Cauchy problems in 2D anisotropic heat conduction

被引：7

作者：

Voinea-Marinescu, Andreea-Paula ^{[1
,2
]}

Marin, Liviu ^{[1
,2
,3
]}

Delvare, Franck ^{[4
,5
,6
]}

机构：

[1] Univ Bucharest, Fac Math & Comp Sci, Dept Math, 14 Acad, Bucharest 010014, Romania

[2] Univ Bucharest, Res Inst Univ Bucharest ICUB, 90-92 Sos Panduri, Bucharest 050663, Romania

[3] Romanian Acad, Gheorghe Mihoc Caius Iacob Inst Math Stat & Appl, 13 Calea 13 Septembrie, Bucharest 050711, Romania

[4] Normandie Univ, F-14032 Caen, France

[5] UNICAEN, LMNO, F-14032 Caen, France

[6] CNRS, UMR 6139, F-14032 Caen, France

来源：

NUMERICAL ALGORITHMS | 2021年 / 88卷 / 04期

关键词：

Inverse problem; Cauchy problem; Anisotropic heat conduction; Fading regularization method algorithm; Boundary element method; BOUNDARY-ELEMENT METHOD; FUNDAMENTAL-SOLUTIONS; COMPLETION;

D O I：

10.1007/s11075-021-01090-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate the numerical reconstruction of the missing thermal boundary data on a part of the boundary for the steady-state heat conduction equation in anisotropic solids from the knowledge of exact or noisy Cauchy data on the remaining and accessible boundary. This inverse boundary value problem is tackled by applying and adapting to the anisotropic case the algorithm based on the fading regularization method, originally proposed by Cimetiere, Delvare, and Pons (Comptes Rendus de l'Academie des Sciences - Serie IIb - Mecanique, 328 639-644 2000), and Cimetiere, Delvare, et al. (Inverse Probl., 17 553-570 2001) for the isotropic heat conduction equation. The numerical implementation is realised for 2D homogeneous solids by using the boundary element method, whilst the numerical solution is stabilized/regularized by stopping the iterative process based on an L-curve type criterion (Hansen 1998).

引用

页码：1667 / 1702

页数：36