A Precise Time-Domain Expanding Boundary-Element Method for Solving Three-Dimensional Transient Heat Conduction Problems with Variable Thermal Conductivity

REFERENCES

• M. N. Özişik , Boundary Values Problems of Heat Conduction , International Textbook Company , Scranton , PA , 1968 .
   Google Scholar
• O. C. Zienkiewicz and R. L. Taylor , The Finite Element Method , McGraw-Hill , London , 1977 .
   Google Scholar
• H. K. Versteeg and W. Malalasekera , The Finite Volume Method: An Introduction to Computational Fluid Dynamics , Pearson Education , Edinburgh Gate , UK , 2007.
   Google Scholar
• W. J. Minkowycz , E. M. Sparrow , and J. Y. Murthy , Handbook of Numerical Heat Transfer , John Wiley , New York , 2006 .
   Google Scholar
• M. N. Özişik , Finite Difference Methods in Heat Transfer , CRC Press , Boca Raton , FL , 1994 .
   Google Scholar
• C. A. Brebbia and J. Dominguez , Boundary Elements An Introductory Course, , 2nd ed. , WIT Press Computational Mechanics Publications , Southampton , UK , 1998 .
   Google Scholar
• O. O. Onyejekwe , A Comparison of Time Discretization Schemes for the Green Element Solution of the Transient Heat Conduction Equation , Numer. Heat Transfer B , vol. 38 , pp. 405 – 422 , 2000 .
   Web of Science ®Google Scholar
• H. T. Yang , A Precise Algorithm in the Time Domain to Solve the Problem of Heat Transfer , Numer. Heat Transfer B , vol. 35 , pp. 243 – 249 , 1999 .
   Web of Science ®Google Scholar
• H. T. Yang and Z. Han , Solving Non-linear Viscoelastic Problems via a Self-adaptive Precise Algorithm in Time Domain , Int. J. Solids Struct , vol. 54 , pp. 5483 – 5498 , 2004 .
   Web of Science ®Google Scholar
• Y. Ren and H. T. Yang , Equivalent Analysis of Orthogonal Viscoelastic Jointed Rock via an Adaptive Algorithm in Time Domain , Finite Elem. Anal. Des. , vol. 46 , pp. 875 – 888 , 2010 .
   Web of Science ®Google Scholar
• H. T. Li , H. T. Yang and N. Li. , An Adaptive Algorithm in Time Domain for Dynamic Analysis of a Simply Supported Beam Subjected to a Moving Vehicle , Math. Meth. Appl. Sci. , vol. 34 , pp. 996 – 1005 , 2011 .
   Web of Science ®Google Scholar
• H. T. Yang and X. Zhao , A Temporally-Piecewise Adaptive Algorithm to Solve Transient Convection-Diffusion Heat Transfer Problems , Comput. Model. Eng. Sci. , vol. 74 , pp. 139 – 159 , 2012 .
   Web of Science ®Google Scholar
• Y. N. Xue and H. T. Yang , A Numerical Method to Estimate Temperature Intervals for Transient Convection-Diffusion Heat Transfer Problems , Int. Commun. Heat Mass Transfer , vol. 47 , pp. 56 – 61 , 2013 .
   Web of Science ®Google Scholar
• Y. Q. He and H. T. Yang , Identification of Geometric Boundary Configurations in Heat Transfer Problems via Element-Free Galerkin and Level-Set Methods , Numer. Heat Transfer B , vol. 55 , pp. 313 – 323 , 2009 .
   Web of Science ®Google Scholar
• H. T. Yang and Y. Liu , A Combined Approach of EFGM and Precise Algorithm in Time Domain Solving Viscoelasticity Problem , Int. J. Solids Struct. , vol. 40 , pp. 701 – 714 , 2003 .
   Web of Science ®Google Scholar
• E. Divo and A. J. Kassab , A Boundary Integral Equation for Steady Heat Conduction in Anisotropic and Heterogeneous Media , Numer. Heat Transfer B , vol. 32 , pp. 37 – 61 , 1997 .
   Web of Science ®Google Scholar
• S. P. Song and B. Q. Li , Boundary Integral Solution of Thermal Radiation Exchanges in Axisymmetric Furnaces , Numer. Heat Transfer B , vol. 44 , pp. 489 – 507 , 2003 .
   Web of Science ®Google Scholar
• A. J. Kassab and L. C. Wrobel , Boundary Element Methods in Heat Conduction , in W. J. Minkowycz and E. M. Sparrow (eds.), Recent Advances in Numerical Heat Transfer , vol. 2 , pp. 143 – 188 , Taylor & Francis , New York , 2000 .
   Google Scholar
• R. P. Shaw , Green's Functions for Heterogeneous Media Potential Problems , Eng. Anal. Bound. Elem. , vol. 13 , pp. 219 – 221 , 1994 .
   Web of Science ®Google Scholar
• D. L. Clements , Fundamental Solutions for Second Order Linear Elliptic Partial Differential Equations , Comput. Mech. , vol. 22 , pp. 26 – 31 , 1998 .
   Web of Science ®Google Scholar
• D. Nardini and C. A. Brebbia , A New Approach for Free Vibration Analysis Using Boundary Elements , Appl. Math. Model. , vol. 7 , pp. 157 – 162 , 1983 .
   Web of Science ®Google Scholar
• P. W. Partridge , C. A. Brebbia , and L. C. Wrobel , The Dual Reciprocity Boundary Element Method , Computational Mechanics Publications , Southampton , UK , 1992 .
   Google Scholar
• S. Gümgüm and M. Tezer-Sezgin , DRBEM Solution of the Natural Convective Flow of Micropolar Fluids , Numer. Heat Transfer A , vol. 57 , pp. 777 – 798 , 2010 .
   Web of Science ®Google Scholar
• N. Alsoy-Akgün and D. Lesnic , A Numerical Solution for an Inverse Natural Magneto-Convection Problem , Numer. Heat Transfer B , vol. 63 , pp. 115 – 138 , 2013 .
   Web of Science ®Google Scholar
• M. A. Fahmy , Transient Magneto-Thermo-Elastic Stresses in an Anisotropic Viscoelastic Solid with and without a Moving Heat Source, Numer. Heat Transfer A , vol. 61, pp. 633–650, 2013.
   Web of Science ®Google Scholar
• M. A. Fahmy , A Three-Dimensional Generalized Magneto-Thermo-Viscoelastic Problem of a Rotating Functionally Graded Anisotropic Solids with and without Energy Dissipation , Numer. Heat Transfer A , vol. 63 , pp. 713 – 733 , 2013 .
   Web of Science ®Google Scholar
• X. W. Gao , The Radial Integration Method for Evaluation of Domain Integrals with Boundary-Only Discretization , Eng. Anal. Bound. Elem. , vol. 26 , pp. 905 – 916 , 2002 .
   Web of Science ®Google Scholar
• X. W. Gao , A Boundary Element Method without Internal Cells for Two-Dimensional and Three-Dimensional Elastoplastic Problems , J. Appl. Mech. , vol. 69 , pp. 154 – 160 , 2002 .
   Web of Science ®Google Scholar
• X. W. Gao , Evaluation of Regular and Singular Domain Integral with Boundary-Only Discretization—Theory and Fortran Code , J. Comput. Appl. Math. , vol. 175 , pp. 265 – 290 , 2005 .
   Web of Science ®Google Scholar
• K. Yang , and X. W. Gao , Radial Integration BEM for Transient Heat Conduction Problems , Eng. Anal. Bound. Elem. , vol. 34 , pp. 557 – 563 , 2010 .
   Web of Science ®Google Scholar
• K. Yang , X. W. Gao , and Y. F. Liu , Using Analytical Expressions in Radial Integration BEM for Variable Coefficient Heat Conduction Problems , Eng. Anal. Bound. Elem. , vol. 35 , pp. 1085 – 1089 , 2011 .
   Web of Science ®Google Scholar
• E. L. Albuquerque , P. Sollero , and W. Portilho de Paiva , The BEM and the RIM in the Dynamic Analysis of Symmetric Laminate Composite Plates , Brazil. Soc. Mech. Sci. Eng. , pp. 41 – 50 , 2007 .
   Google Scholar
• X. W. Gao , C. Zhang , and L. Guo , Boundary-Only Element Solutions of 2D and 3D Nonlinear and Nonhomogeneous Elastic Problems , Eng. Anal. Bound. Elem. , vol. 31 , pp. 974 – 982 , 2007 .
   Web of Science ®Google Scholar
• C. Zhang , M. Cui , J. Wang , X. W. Gao , J. Sladek , and V. Sladek , 3D Crack Analysis in Functionally Graded Materials , Eng. Fract. Mech. , vol. 78 , pp. 585 – 604 , 2011 .
   Web of Science ®Google Scholar
• H. F. Peng , M. Cui , and X. W. Gao , A Boundary Element Method without Internal Cells for Solving Viscous Fow Problems , Eng. Anal. Bound. Elem. , vol. 37 , pp. 293 – 300 , 2013 .
   Web of Science ®Google Scholar
• B. Yu , W. A Yao , X. W. Gao , and S. Zhang , Radial Integration BEM for One-Phase Solidification Problems , Eng. Anal. Bound. Elem. , vol. 39 , pp. 36 – 43 , 2014 .
   Web of Science ®Google Scholar
• M. A. AL-Jawary and L. C. Wrobel , Radial Integration Boundary Integral and Integro-differential Equation Methods for Two-Dimensional Heat Conduction Problems with Variable Coefficients , Eng. Anal. Bound. Elem. , vol. 36 , pp. 685 – 695 , 2012 .
   Web of Science ®Google Scholar
• B. Yu , W. A. Yao , X. W Gao , and Q. Gao , A Combined Approach of RIBEM and Precise Time Integration Algorithm for Solving Transient Heat Conduction Problems , Numer. Heat Transfer B , vol. 65 , pp. 155 – 173 , 2014 .
   Web of Science ®Google Scholar
• S. R. Karur and P. A. Ramachandran , Augmented Thin Plate Spline Approximation in DRM , Bound. Elem. Commun. , vol. 6 , pp. 55 – 58 , 1995 .
   Google Scholar
• M. N. Özişik , Heat Conduction , John Wiley , New York , 1993 .
   Google Scholar