Application of the method of fundamental solutions and radial basis functions for inverse transient heat source problem

Mierzwiczak, Magdalena; Kołodziej, Jan Adam

doi:10.1016/j.cpc.2010.08.020

Cited by 34 publications

(11 citation statements)

References 61 publications

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“…Although the MFS has been widely used for analysis of heat conduction problems in different conditions (e.g. Ahmadabadi et al, 2009;Kołodziej et al, 2010;Mierzwiczak and Kołodziej, 2012); however, to the authors' knowledge, the MFS formulation for analysis of internal curve line/surface heat sources has not been presented yet. The method presented here can be simply employed without considering any internal points/nodes and, therefore, it preserves the attractiveness of the MFS as a boundary--type mesh-free method.…”

Section: Introductionmentioning

confidence: 99%

An efficient analysis of steady-state heat conduction involving curved line/surface heat sources in two/three-dimensional isotropic media

Mohammadi

Hematiyan

Shiah³

2018

jtam

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In this paper, a new formulation based on the method of fundamental solutions for two/three-dimensional steady-state heat conduction problems involving internal curved line/surface heat sources is presented. Arbitrary shapes and non-uniform intensities of the curved heat sources can be modeled by an assemblage of several parts with quadratic variations. The presented mesh-free modeling does not require any internal points as in domain methods. Four numerical examples are studied to verify the validity and efficiency of the proposed method. Our analyses have shown that the presented mesh-free formulation is very efficient in comparison with conventional boundary or domain solution techniques.

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Section: Introductionmentioning

confidence: 99%

An efficient analysis of steady-state heat conduction involving curved line/surface heat sources in two/three-dimensional isotropic media

Mohammadi

Hematiyan

Shiah³

2018

jtam

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“…Paper [16] discusses the solution of the inverse problem for the Poisson equation with the use of fundamental solution method and Tikhonov regularization. Application of the fundamental solutions method for solving the inverse problem of heat source determination in an unsteady heat conduction is presented in [15].…”

Section: Plusmentioning

confidence: 99%

“…Coefficients α j were introduced into the solution (15). Hence, For measuring points ξ * l , where l = 1, 2, .…”

Section: Inverse Problemmentioning

confidence: 99%

Non-linear unsteady inverse boundary problem for heat conduction equation

Joachimiak¹,

Ciałkowski²

2017

Archives of Thermodynamics

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Direct and inverse problems for unsteady heat conduction equation for a cylinder were solved in this paper. Changes of heat conduction coefficient and specific heat depending on the temperature were taken into consideration. To solve the non-linear problem, the Kirchhoff's substitution was applied. Solution was written as a linear combination of Chebyshev polynomials. Sensitivity of the solution to the inverse problem with respect to the error in temperature measurement and thermocouple installation error was analysed. Temperature distribution on the boundary of the cylinder, being the numerical example presented in the paper, is similar to that obtained during heating in the nitrification process.Keywords: Inverse problem; Sensitivity of the solution to the inverse problem; Application of Chebyshev polynomials

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“…Configurations studied in both previous references are related to boundary heat flux identification considering a 1D mathematical model. In the works of Kolodziej et al (2010) or Mierzwiczak and Kolodziej (2010;, the method of fundamental solutions was successfully implemented for an IHCP. This meshless method is relatively new and is an attractive alternative to the finite or boundary element methods.…”

Section: Introductionmentioning

confidence: 99%

Heating source localization in a reduced time

Beddiaf

Autrique

Perez

et al. 2016

International Journal of Applied Mathematics and Computer Science

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Inverse three-dimensional heat conduction problems devoted to heating source localization are ill posed. Identification can be performed using an iterative regularization method based on the conjugate gradient algorithm. Such a method is usually implemented off-line, taking into account observations (temperature measurements, for example). However, in a practical context, if the source has to be located as fast as possible (e.g., for diagnosis), the observation horizon has to be reduced. To this end, several configurations are detailed and effects of noisy observations are investigated.

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Application of the method of fundamental solutions and radial basis functions for inverse transient heat source problem

Cited by 34 publications

References 61 publications

An efficient analysis of steady-state heat conduction involving curved line/surface heat sources in two/three-dimensional isotropic media

An efficient analysis of steady-state heat conduction involving curved line/surface heat sources in two/three-dimensional isotropic media

Non-linear unsteady inverse boundary problem for heat conduction equation

Heating source localization in a reduced time

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