On efficient reconstruction of boundary data with optimal placement of the source points in the MFS: application to inverse Stefan problems

References

• Rubinstein LI . The Stefan problem. Providence (RI): American Mathematical Society; 1971. Translated from the Russian by Solomon AD.Translations of Mathematical Monographs, Vol. 27.
   Google Scholar
• Gol’dman NL . Inverse Stefan problems. Vol. 412, Mathematics and its applications. Dordrecht: Kluwer Academic Publishers Group; 1997.
   Google Scholar
• Słota D . Identification of the cooling condition in 2D and 3D continuous casting processes. Num Heat Trans B. 2009;55:155–176.
   Web of Science ®Google Scholar
• Słota D . Reconstruction of the boundary condition in the problem of the binary alloy solidification. Arch Metall Mater. 2011;56:279–285.
   Web of Science ®Google Scholar
• Wang Z , Yao M , Wang X , et al. Inverse problem-coupled heat transfer model for steel continuous casting. J Mater Proc Tech. 2014;214:44–49.
   Web of Science ®Google Scholar
• O’Mahoney D , Browne DJ . Use of an experiment and an inverse method to study interface heat transfer during solidification in the investment casting process. Exp Thermal Fluid Sci. 2000;22:111–122.
   Web of Science ®Google Scholar
• Okamoto K , Li BQ . A regularization method for the inverse design of solidification processes with natural convection. Int J Heat Mass Transfer. 2007;50:4409–4423.
   Web of Science ®Google Scholar
• Chantasiriwan S , Johansson BT , Lesnic D . The method of fundamental solutions for free surface Stefan problems. Eng Anal Bound Elem. 2009;33(4):529–538.
   Web of Science ®Google Scholar
• Johansson BT , Lesnic D , Reeve T . A method of fundamental solutions for the one-dimensional inverse Stefan problem. App Math Modell. 2011;35:4367–4378.
   Web of Science ®Google Scholar
• Johansson BT , Lesnic D , Reeve T . The method of fundamental solutions for the two-dimensional inverse Stefan problem. Inverse Probl Sci Eng. 2014;22:112–129.
   Web of Science ®Google Scholar
• Karageorghis A , Lesnic D , Marin L . A survey of applications of the MFS to inverse problems. Inverse Probl Sci Eng. 2011;19(3):309–336.
   Web of Science ®Google Scholar
• Mathon R , Johnston RL . The approximate solution of elliptic boundary-value problems by fundamental solutions. SIAM J Numer Anal. 1977;14(4):638–650.
   Web of Science ®Google Scholar
• Johnston RL , Fairweather G . The method of fundamental solutions for problems in potential flow. Appl Math Modell. 1984;8(4):265–270.
   Web of Science ®Google Scholar
• Fairweather G , Karageorghis A . The method of fundamental solutions for elliptic boundary value problems. Adv Comput Math. 1998;9(1–2):69–95.
   Web of Science ®Google Scholar
• Gorzelaczyk P , Koodziej JA . Some remarks concerning the shape of the source contour with application of the method of fundamental solutions to elastic torsion of prismatic rods. Eng Anal Boundary Elem. 2008;32(1):64–75.
   Web of Science ®Google Scholar
• Alves CJS . On the choice of source points in the method of fundamental solutions. Eng Anal Bound Elem. 2009;33(12):1348–1361.
   Web of Science ®Google Scholar
• Cisilino AP , Sensale B . Application of a simulated annealing algorithm in the optimal placement of the source points in the method of the fundamental solutions. Comput Mech. 2002;28(2):129–136.
   Web of Science ®Google Scholar
• Karageorghis A . A practical algorithm for determining the optimal pseudo-boundary in the method of fundamental solutions. Adv Appl Math Mech. 2009;1(4):510–528.
   Web of Science ®Google Scholar
• Wong KY , Ling L . Optimality of the method of fundamental solutions. Eng Anal Bound Elem. 2011;35(1):42–46.
   Web of Science ®Google Scholar
• Chen CS , Karageorghis A , Li Y . On choosing the location of the sources in the MFS. Numer Algorithms. 2016;72(1):107–130.
   Web of Science ®Google Scholar
• Cannon JR , Douglas J Jr . The Cauchy problem for the heat equation. SIAM J Numer Anal. 1967;4:317–336.
   Google Scholar
• Cannon JR , Primicerio M . Remarks on the one-phase Stefan problem for the heat equation with the flux prescribed on the fixed boundary. J Math Anal Appl. 1971;35(2):361–373.
   Web of Science ®Google Scholar
• Cannon JR , Hill CD . Existence, uniqueness, stability, and monotone dependence in a Stefan problem for the heat equation. J Math Mech. 1967;17(17):1–19.
   Google Scholar
• Chen CS , Cho HA , Golberg MA . Some comments on the ill-conditioning of the method of fundamental solutions. Eng Anal Boundary Element. 2006;30(5):405–410.
   Web of Science ®Google Scholar
• Ramachandran PA . Method of fundamental solutions: singular value decomposition analysis. Commun Numer Methods Eng. 2002;18(11):789–801.
   Web of Science ®Google Scholar
• Ang DD , Dinh APN , Thanh DN . An inverse Stefan problem: identification of boundary value. J Comput Appl Math. 1996;66(1):75–84.
   Web of Science ®Google Scholar
• Andrews JG , Atthey DR . On the motion of an intensely heated evaporating boundary. J Inst Math Appl. 1975;15:59–72.
   Google Scholar
• Chen Y-K , Milos FS . Ablation and thermal response program for spacecraft heatshield analysis. J Spacecraft Rockets. 1999;36(3):475–483.
   Web of Science ®Google Scholar
• Campbell AJ , Humayun M . Trace element microanalysis in iron meteorites by laser ablation ICPMS. Anal Chem. 1999;71(5):939–946.
   PubMed Web of Science ®Google Scholar
• Lin W-S . Steady ablation on the surface of a two-layer composite. Int J Heat Mass Trans. 2005;48(25–26):5504–5519.
   Web of Science ®Google Scholar
• Tayler AB . Mathematical models in applied mechanics. Oxford: Oxford University Press; 2001.
   Google Scholar
• Johnson WD . The profile of maturity in alpine glacial erosion. J Geology. 1904;12(7):569–578.
   Google Scholar
• Namenanee K , McKenzie J , Kosa E , et al . A new approach for catheter ablation of atrial fibrillation: mapping of the electrophysiologic substrate. J Amer College Cardiol. 2004;43(11):2044–2053.
   PubMed Web of Science ®Google Scholar