The multiple-scale polynomial Trefftz method for solving inverse heat conduction problems

2016 ◽  
Vol 95 ◽  
pp. 936-943 ◽  
Author(s):  
Chein-Shan Liu ◽  
Chung-Lun Kuo ◽  
Wun-Sin Jhao
Keyword(s):  
Heat Conduction ◽  
Multiple Scale ◽  
Inverse Heat Conduction ◽  
Trefftz Method ◽  
Inverse Heat Conduction Problems

scholarly journals On Solving Two-Dimensional Inverse Heat Conduction Problems Using the Multiple Source Meshless Method

2019 ◽  
Vol 9 (13) ◽  
pp. 2629 ◽  
Author(s):  
Ku ◽  
Xiao ◽  
Huang ◽  
Yeih ◽  
Liu
Keyword(s):  
Heat Conduction ◽  
Meshless Method ◽  
Domain Decomposition Method ◽  
Domain Boundary ◽  
Addition Theorem ◽  
Two Dimensions ◽  
Multiple Source ◽  
Inverse Heat Conduction ◽  
Trefftz Method ◽  
Inverse Heat Conduction Problems

In this article, a newly developed multiple-source meshless method (MSMM) capable of solving inverse heat conduction problems in two dimensions is presented. Evolved from the collocation Trefftz method (CTM), the MSMM approximates the solution by using many source points through the addition theorem such that the ill-posedness is greatly reduced. The MSMM has the same superiorities as the CTM, such as the boundary discretization only, and is advantageous for solving inverse problems. Several numerical examples are conducted to validate the accuracy of solving inverse heat conduction problems using boundary conditions with different levels of noise. Moreover, the domain decomposition method is adopted for problems in the doubly-connected domain. The results demonstrate that the proposed method may recover the unknown data with remarkably high accuracy, even though the over-specified boundary data are assigned a portion that is less than 1/10 of the overall domain boundary.

Efficient Numerical Solution of Inverse Heat Conduction Problems

1995 ◽  
Author(s):  
Hans-Jürgen Reinhardt ◽  
Dinh Nho Hao
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Numerical Methods ◽  
Stationary Point ◽  
Forthcoming Paper ◽  
Inverse Heat Conduction ◽  
Piecewise Constant ◽  
Numerical Tests ◽  
Inverse Heat Conduction Problems ◽  
Special Case

Abstract In this contribution we propose new numerical methods for solving inverse heat conduction problems. The methods are constructed by considering the desired heat flux at the boundary as piecewise constant (in time) and then deriving an explicit expression for the solution of the equation for a stationary point of the minimizing functional. In a very special case the well-known Beck method is obtained. For the time being, numerical tests could not be included in this contribution but will be presented in a forthcoming paper.

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