Numerical simulation of the heat conduction in composite materials

References

• Boyle , J. , Mihajlovic , J. and Scott , J. 2009 . HSL_MI20: An efficient AMG preconditioner for finite element problems in 3D . Int. J. Numer. Math. Engng , Doi:10.1002/nme.2758. (Published online 24 August 2009)
   Google Scholar
• Bryan , K. and Caudill , L. 1996 . An inverse problem in thermal imaging . SIAM J. Appl. Math., , 59 : 715 – 735 . Doi:10.1137/S0036139994277828
   Google Scholar
• Ciarlet , P. , Schultz , M. and Varga , R. 1968 . Numerical methods of high‐order accuracy for nonlinear baoundary value problems . Numerische Mathematik, , 11 : 331 – 345 . Doi:10.1007/BF02166686
   Google Scholar
• Čiegis , R. , Gaspar , F. and Rodrigo , C. 2008 . On parallel multiblock geometric multigrid algorithm . Computational Methods in Applied Mathematics, , 8 (3) : 223 – 236 .
   Google Scholar
• Čiegis , R. , Ilgevičius , A. , Liess , H. , Meilūnas , M. and Suboč , O. 2007 . Numerical simulation of the heat conduction in electrical cables . Math. Model. Anal., , 12 (4) : 425 – 439 . Doi:10.3846/1392–6292.2007.12.425–439.
   Web of Science ®Google Scholar
• Čiegis , Raim. , Čiegis , Rem. , Meilūnas , M. , Jankevičiūte , G. and Starikovičius , V. 2008 . Parallel numerical algorithm for optimization of electrical cables . Math. Model. Anal., , 13 (4) : 471 – 482 .
   Web of Science ®Google Scholar
• Ekeland , I. and Temam , R. 1976 . Convex Analysis and Variational Problems. , Amsterdam, New York, Oxford : North‐Holland .
   Google Scholar
• Ewing , R. , Iliev , O. and Lazarov , R. 2001 . A modified finite volume approximation of second order elliptic with discontinuous coefficients . SIAM J. Sci. Comp., , 23 (4) : 1334 – 13350 . Doi:10.1137/S1064827599353877
   Web of Science ®Google Scholar
• Hu , X. , Xu , X. and Chen , W. 2009 . Numerical method for the inverse heat transfer problem in composite materials with Stefan‐Boltzmann conditions . Adv. Com‐put. Math., , Doi:10.1007/s10444–009–9131‐x. (Published online 30 May 2009)
   Google Scholar
• Incropera , F. , DeWitt , P. and David , P. 1985 . Introduction to Heat Transfer. , New York : John Willey & Sons .
   Google Scholar
• Jankevičiūte , G. and Čiegis , R. 2009 . “ Parallel numerical solver for the simulation of the heat conduction in electrical cables. ” . In Parallel Linear Algebra and Optimization: Advances and Applications. Springer Optimization and Its Applications , Edited by: Čiegis , R. , Henty , D. , Kagstrōm , B. and Žilinskas , J. volume 27 , 211 – 216 . New‐York : Springer . ISBN: 978–0–387–09706–0
   Google Scholar
• Liu , L. , Huang , M. , Yuan , K. and Križek , M. 2009 . Numerical approximation of a nonlinear 3D heat radiation problem . Adv. Appl. Math. Mech., , 1 (1) : 125 – 139 .
   Google Scholar
• Notay , Y. 2009 . An aggregation‐based algebraic multigrid method . Electronic Transactions on Numerical Analysis , (accepted for publication)
   Google Scholar
• Notay , Y. and Vassilevski , P. 2008 . Recursive krylov‐based multigrid cycles . Numer. Lin. Alg. Appl., , 15 : 473 – 487 .
   Google Scholar
• Saad , Y. 2003 . Iterative Methods for Sparse Linear Systems. , Philadelphia, PA : SIAM .
   Google Scholar
• Samarskii , A.A. 2001 . The Theory of Difference Schemes. New York‐Basel : Marcel Dekker Inc., .
   Google Scholar
• Stüben , K. 2001 . A review of algebraic multigrid. J . Comput. and Appl. Math., , 128 : 281 – 309 . Doi:10.1016/S0377–0427(00)00516–1.
   Web of Science ®Google Scholar
• Yang , G. , Yamamoto , M. and Cheng , J. 2007 . Heat transfer in composite materials with Stefan‐Boltzmann interface conditions . Math. Methods Appl. Sci., , 31 : 1297 – 1314 .
   Google Scholar