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Inverse Problems in Science and Engineering Volume 16, 2008 - Issue 8: Inverse Problems, Design and Optimization (IPDO2007) Symposium, Miami Beach, Florida, USA, April 16–18, 2007
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Original Articles

Recovering the source term in a linear diffusion problem by the method of fundamental solutions

Carlos J.S. AlvesCEMAT and Department of Mathematics, Instituto Superior Técnico (TULisbon), Lisbon, Portugal
,
Marcelo J. ColaçoDepartment of Mechanical Engineering, Military Institute of Engineering, Rio de Janeiro, RJ, Brazil
,
Vitor M.A. LeitãoICIST and Department of Civil Engineering and Archit., Instituto Superior Técnico (TULisbon), Lisboa, Portugal
,
Nuno F.M. MartinsCEMAT-IST and Department of Mathematics, Fac. Ciências e Tecnologia (UNLisbon), Quinta da Torre, Caparica, Portugal
,
Helcio R.B. OrlandeDepartment of Mechanical Engineering, Federal University of Rio de Janeiro, Rio de Janeiro, RJ, Brazil
&
Nilson C. RobertyProgram of Nuclear Engineering, Federal University of Rio de Janeiro, Rio de Janeiro, RJ, Brazil
Pages 1005-1021 | Received 16 Apr 2007, Accepted 30 Nov 2007, Published online: 08 Nov 2008

Citations (31)

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Gustavo R. Gasperazzo & Marcelo J. Colaço. (2023) Transient Source Terms Estimate in Advection-Diffusion Problems Using the Method of Fundamental Solutions and an Eulerian-Lagrangian Transformation. Heat Transfer Engineering 0:0, pages 1-14.
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Malihe Rostamian & Alimardan Shahrezaee. (2018) A meshless method for solving 1D time-dependent heat source problem. Inverse Problems in Science and Engineering 26:1, pages 51-82.
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Malihe Rostamian & Alimardan Shahrezaee. (2017) A meshless method to the numerical solution of an inverse reaction–diffusion–convection problem. International Journal of Computer Mathematics 94:3, pages 597-619.
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Andrzej Frąckowiak, Nikolai D. Botkin, Michał Ciałkowski & Karl-Heinz Hoffmann. (2015) Iterative algorithm for solving the inverse heat conduction problems with the unknown source function. Inverse Problems in Science and Engineering 23:6, pages 1056-1071.
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Marcelo J. Colaço, Carlos J.S. Alves & Helcio R.B. Orlande. (2015) Transient non-intrusive method for estimating spatial thermal contact conductance by means of the reciprocity functional approach and the method of fundamental solutions. Inverse Problems in Science and Engineering 23:4, pages 688-717.
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Yan Gu, Wen Chen & Zhuo-Jia Fu. (2014) Singular boundary method for inverse heat conduction problems in general anisotropic media. Inverse Problems in Science and Engineering 22:6, pages 889-909.
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Nuno F.M. Martins. (2012) An iterative shape reconstruction of source functions in a potential problem using the MFS. Inverse Problems in Science and Engineering 20:8, pages 1175-1193.
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Denis M. de Sousa & Nilson C. Roberty. (2012) An inverse source problem for the stationary diffusion–advection–decay equation. Inverse Problems in Science and Engineering 20:7, pages 891-915.
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M. Mierzwiczak & J.A. Kołodziej. (2011) The determination of heat sources in two dimensional inverse steady heat problems by means of the method of fundamental solutions. Inverse Problems in Science and Engineering 19:6, pages 777-792.
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A. Karageorghis, D. Lesnic & L. Marin. (2011) A survey of applications of the MFS to inverse problems. Inverse Problems in Science and Engineering 19:3, pages 309-336.
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Articles from other publishers (21)

Moncef Mahjoub & Ridha Mdimagh. (2023) The inverse problem of dipolar source identification from incomplete boundary measurements. Mathematical Methods in the Applied Sciences.
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Lekbir Afraites, Chorouk Masnaoui & Mourad Nachaoui. (2022) Shape optimization method for an inverse geometric source problem and stability at critical shape. Discrete & Continuous Dynamical Systems - S 15:1, pages 1.
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Jinhui Jiang, M. Shadi Mohamed, Mohammed Seaid & Hongqiu Li. (2020) Fast inverse solver for identifying the diffusion coefficient in time-dependent problems using noisy data. Archive of Applied Mechanics 91:4, pages 1623-1639.
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Andrzej Frąckowiak, Aleksander Olejnik, Agnieszka Wróblewska & Michał Ciałkowski. (2020) Application of the Protective Coating for Blade’s Thermal Protection. Energies 14:1, pages 50.
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A. Frąckowiak, J. v. Wolfersdorf & M. Ciałkowski. (2019) Optimization of cooling of gas turbine blades with channels filled with porous material. International Journal of Thermal Sciences 136, pages 370-378.
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Bo Yu, Chuang Xu, Weian Yao & Zeng Meng. (2018) Estimation of boundary condition on the furnace inner wall based on precise integration BEM without iteration. International Journal of Heat and Mass Transfer 122, pages 823-845.
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Carlos J. S. Alves, Roberto Mamud, Nuno F. M. Martins & Nilson C. Roberty. (2017) On Inverse Problems for Characteristic Sources in Helmholtz Equations. Mathematical Problems in Engineering 2017, pages 1-16.
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J. Rocha de Faria & D. Lesnic. (2014) Topological Derivative for the Inverse Conductivity Problem: A Bayesian Approach. Journal of Scientific Computing 63:1, pages 256-278.
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Joshua C. Chang, Van M. Savage & Tom Chou. (2014) A Path-Integral Approach to Bayesian Inference for Inverse Problems Using the Semiclassical Approximation. Journal of Statistical Physics 157:3, pages 582-602.
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Nuno Martins. (2014) Detecting the localization of elastic inclusions and Lamé coefficients. Inverse Problems and Imaging 8:3, pages 779-794.
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Carlos J S Alves, Nuno F M Martins & Nilson C Roberty. (2014) Identification and reconstruction of elastic body forces. Inverse Problems 30:5, pages 055015.
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Nuno F. M. Martins. (2014) Detecting the localization of elastic inclusions and Lamé coefficients. Inverse Problems & Imaging 8:3, pages 779-794.
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Marcelo J. Colaço & Carlos J.S. Alves. (2013) A fast non-intrusive method for estimating spatial thermal contact conductance by means of the reciprocity functional approach and the method of fundamental solutions. International Journal of Heat and Mass Transfer 60, pages 653-663.
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Zhi-jie Gu & Yong-ji Tan. (2012) Fundamental solution method for inverse source problem of plate equation. Applied Mathematics and Mechanics 33:12, pages 1513-1532.
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Mejdi Azaı¨ez, Faker Ben Belgacem & Faten Jelassi. (2011) The density function reconstruction of surface sources from a single Cauchy measurement. Computers & Fluids 43:1, pages 14-22.
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Liviu Marin, Andreas Karageorghis & Daniel Lesnic. (2011) The MFS for numerical boundary identification in two-dimensional harmonic problems. Engineering Analysis with Boundary Elements 35:3, pages 342-354.
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A. Karageorghis. (2010) Efficient MFS Algorithms for Inhomogeneous Polyharmonic Problems. Journal of Scientific Computing 46:3, pages 519-541.
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Magdalena Mierzwiczak & Jan Adam Kołodziej. (2010) Application of the method of fundamental solutions and radial basis functions for inverse transient heat source problem. Computer Physics Communications 181:12, pages 2035-2043.
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Y.C. Hon, M. Li & Y.A. Melnikov. (2010) Inverse source identification by Green's function. Engineering Analysis with Boundary Elements 34:4, pages 352-358.
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Nilson C. Roberty & Marcelo L. S. Rainha. (2010) Moving Heat Source Reconstruction from the Cauchy Boundary Data. Mathematical Problems in Engineering 2010, pages 1-22.
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F Ben Belgacem & F Jelassi. (2009) Identifiability of surface sources from Cauchy data. Inverse Problems 25:7, pages 075007.
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