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International Journal of Computer Mathematics Volume 88, 2011 - Issue 8
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Section B

A method of fundamental solutions for two-dimensional heat conduction

B. Tomas Johansson School of Mathematics, University of Birmingham, Birmingham, B15 2TT, UKCorrespondence[email protected]
,
Daniel Lesnic Department of Applied Mathematics, University of Leeds, Leeds, LS2 9JT, UK
&
Thomas Reeve School of Mathematics, University of Birmingham, Birmingham, B15 2TT, UK
Pages 1697-1713 | Received 11 Dec 2009, Accepted 27 Aug 2010, Published online: 14 Mar 2011

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W. B. da Silva, J. C. S. Dutra, C. E. P. Kopperschimidt, D. Lesnic & R. G. Aykroyd. (2021) Sequential estimation of the time-dependent heat transfer coefficient using the method of fundamental solutions and particle filters. Inverse Problems in Science and Engineering 29:13, pages 3322-3341.
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Chein-Shan Liu & Chih-Wen Chang. (2020) Analytic series solutions of 2D forward and backward heat conduction problems in rectangles and a new regularization. Inverse Problems in Science and Engineering 28:10, pages 1384-1406.
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Yue Guan, Rade Grujicic, Xuechuan Wang, Leiting Dong & Satya N. Atluri. (2020) A new meshless “fragile points method” and a local variational iteration method for general transient heat conduction in anisotropic nonhomogeneous media. Part II: Validation and discussion. Numerical Heat Transfer, Part B: Fundamentals 78:2, pages 86-109.
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B. Tomas Johansson, Daniel Lesnic & Thomas Reeve. (2014) The method of fundamental solutions for the two-dimensional inverse Stefan problem. Inverse Problems in Science and Engineering 22:1, pages 112-129.
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Michael Dawson, Duncan Borman, Robert B. Hammond, Daniel Lesnic & Dominic Rhodes. (2012) Detection of a two-dimensional moving cavity. International Journal of Computer Mathematics 89:11, pages 1569-1582.
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B. Tomas Johansson, Daniel Lesnic & Thomas Reeve. (2012) A method of fundamental solutions for radially symmetric and axisymmetric backward heat conduction problems. International Journal of Computer Mathematics 89:11, pages 1555-1568.
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B. Tomas Johansson, Daniel Lesnic & Thomas Reeve. (2011) Numerical approximation of the one-dimensional inverse Cauchy–Stefan problem using a method of fundamental solutions. Inverse Problems in Science and Engineering 19:5, pages 659-677.
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S. B. Sorokin. (2023) A Difference Method for Calculating the Heat Flux on an Inaccessible Boundary in a Heat Conduction Problem. Journal of Applied and Industrial Mathematics 17:3, pages 651-663.
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F. Mostajeran & R. Mokhtari. (2022) DeepBHCP: Deep neural network algorithm for solving backward heat conduction problems. Computer Physics Communications 272, pages 108236.
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Nuno F.M. Martins & Pedro Mota. (2022) An adapted plane waves method for heat conduction problems. Applied Mathematics and Computation 415, pages 126689.
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Mehrdad Mohammadi. (2019) The Method of Fundamental Solutions for Two- and Three-Dimensional Transient Heat Conduction Problems Involving Point and Curved Line Heat Sources. Iranian Journal of Science and Technology, Transactions of Mechanical Engineering 45:4, pages 993-1005.
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Kamal Shanazari & Nasrin Mohammadi. (2021) An overlapping domain decomposition Schwarz method applied to the method of fundamental solution. Computational and Applied Mathematics 40:8.
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Yue Guan & Satya N. Atluri. (2021) Meshless fragile points methods based on Petrov‐Galerkin weak‐forms for transient heat conduction problems in complex anisotropic nonhomogeneous media. International Journal for Numerical Methods in Engineering 122:16, pages 4055-4092.
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Jakub Krzysztof Grabski. (2021) On the sources placement in the method of fundamental solutions for time-dependent heat conduction problems. Computers & Mathematics with Applications 88, pages 33-51.
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M. Mohammadi & M.R. Hematiyan. (2021) Analysis of transient uncoupled thermoelastic problems involving moving point heat sources using the method of fundamental solutions. Engineering Analysis with Boundary Elements 123, pages 122-132.
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W.B. da Silva, J.C.S. Dutra, C.E.P. Kopperschimidt, D. Lesnic & R.G. Aykroyd. (2021) Sequential particle filter estimation of a time-dependent heat transfer coefficient in a multidimensional nonlinear inverse heat conduction problem. Applied Mathematical Modelling 89, pages 654-668.
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Lyubomir Boyadjiev, Kamal Rashedi & Mourad Sini. (2019) Estimation of the Time-Dependent Body Force Needed to Exert on a Membrane to Reach a Desired State at the Final Time. Computational Methods in Applied Mathematics 19:2, pages 323-339.
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G. Tsedendorj & H. Isshiki. (2019) Numerical study of unsteady diffusion in circle. Computational and Applied Mathematics 38:1.
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Kamal Rashedi & Aydin Sarraf. (2018) Heat source identification of some parabolic equations based on the method of fundamental solutions. The European Physical Journal Plus 133:10.
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Saeed Sarabadan, Kamal Rashedi & Hojatollah Adibi. (2017) Boundary Determination of the Inverse Heat Conduction Problem in One and Two Dimensions via the Collocation Method Based on the Satisfier Functions. Iranian Journal of Science and Technology, Transactions A: Science 42:2, pages 827-840.
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Yung-Wei Chen. (2018) A highly accurate backward-forward algorithm for multi-dimensional backward heat conduction problems in fictitious time domains. International Journal of Heat and Mass Transfer 120, pages 499-514.
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Jakub Krzysztof Grabski, Daniel Lesnic & B. Tomas Johansson. (2016) Identification of a time-dependent bio-heat blood perfusion coefficient. International Communications in Heat and Mass Transfer 75, pages 218-222.
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Kamal Rashedi, Hojatollah Adibi & Mehdi Dehghan. (2015) Efficient numerical methods for boundary data and right-hand side reconstructions in elliptic partial differential equations. Numerical Methods for Partial Differential Equations 31:6, pages 1995-2026.
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Matthias Augustin, Mathias Bauer, Christian Blick, Sarah Eberle, Willi Freeden, Christian Gerhards Maxim Ilyasov, René Kahnt, Matthias Klug, Sandra Möhringer, Thomas Neu, Helga Nutz, Isabel Michel née Ostermann & Alessandro Punzi. 2015. Handbook of Geomathematics. Handbook of Geomathematics 1547 1629 .
Matthias Albert AugustinMatthias Albert Augustin. 2015. A Method of Fundamental Solutions in Poroelasticity to Model the Stress Field in Geothermal Reservoirs. A Method of Fundamental Solutions in Poroelasticity to Model the Stress Field in Geothermal Reservoirs 115 208 .
Matthias Albert AugustinMatthias Albert Augustin. 2015. A Method of Fundamental Solutions in Poroelasticity to Model the Stress Field in Geothermal Reservoirs. A Method of Fundamental Solutions in Poroelasticity to Model the Stress Field in Geothermal Reservoirs 91 114 .
Matthias Albert AugustinMatthias Albert Augustin. 2015. A Method of Fundamental Solutions in Poroelasticity to Model the Stress Field in Geothermal Reservoirs. A Method of Fundamental Solutions in Poroelasticity to Model the Stress Field in Geothermal Reservoirs 1 9 .
Kamal Rashedi, Hojatollah Adibi, Jamal Amani Rad & Kourosh Parand. (2014) Application of meshfree methods for solving the inverse one-dimensional Stefan problem. Engineering Analysis with Boundary Elements 40, pages 1-21.
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Willi Freeden & Helga Nutz. 2014. Handbuch Tiefe Geothermie. Handbuch Tiefe Geothermie 125 221 .
Matthias Augustin, Mathias Bauer, Christian Blick, Sarah Eberle, Willi Freeden, Christian Gerhards, Maxim Ilyasov, René Kahnt, Matthias Klug, Sandra Möhringer, Thomas Neu, Helga Nutz, Isabel Michel née Ostermann & Alessandro Punzi. 2014. Handbook of Geomathematics. Handbook of Geomathematics 1 74 .
Matthias Augustin, Mathias Bauer, Christian Blick, Sarah Eberle, Willi Freeden, Christian Gerhards, Maxim Ilyasov, René Kahnt, Matthias Klug, Sandra Möhringer, Thomas Neu, Helga Nutz, Isabel Michel née Ostermann & Alessandro Punzi. 2020. Handbook of Geomathematics. Handbook of Geomathematics 1 74 .
Michael Dawson, Duncan Borman, Robert B. Hammond, Daniel Lesnic & Dominic Rhodes. (2013) A meshless method for solving a two‐dimensional transient inverse geometric problem. International Journal of Numerical Methods for Heat & Fluid Flow 23:5, pages 790-817.
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Thomas Reeve & B. Tomas Johansson. (2013) The method of fundamental solutions for a time-dependent two-dimensional Cauchy heat conduction problem. Engineering Analysis with Boundary Elements 37:3, pages 569-578.
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B. Tomas Johansson, Daniel Lesnic & Thomas Reeve. (2012) A method of fundamental solutions for the radially symmetric inverse heat conduction problem. International Communications in Heat and Mass Transfer 39:7, pages 887-895.
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