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Numerical Heat Transfer, Part B: Fundamentals
An International Journal of Computation and Methodology
Volume 64, 2013 - Issue 6
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Original Articles

Numerical Simulation of Heat Conduction Problems by a New Fast Multipole Hybrid Boundary-Node Method

, &
Pages 436-459 | Received 29 Jan 2013, Accepted 18 Jul 2013, Published online: 14 Oct 2013

REFERENCES

  • T. Belytschko , Y. Y. Lu , and L. Gu , Element Free Galerkin Methods , Int. J. Numer. Meth. Eng. , vol. 37 , pp. 229 – 256 , 1994 .
  • S. N. Atluri and T. Zhu , A New Meshless Local Petrov-Galerkin Approach in Computational Mechanics , Comput. Mech. , vol. 22 , pp. 117 – 127 , 1998 .
  • Y. X. Mukherjee and S. Mukherjee , The Boundary Node Method for Potential Problems , Int. J. Numer. Meth. Eng. , vol. 40 , pp. 797 – 815 , 1997 .
  • M. K. Chati , S. Mukherjee , and Y. X. Mukherjee , The Boundary Node Method for Three-Dimensional Linear Elasticity , Int. J. Numer. Meth. Eng. , vol. 46 , pp. 1163 – 1184 , 1999 .
  • X. L. Li and J. Zhu , A Galerkin Boundary Node Method and its Convergence Analysis , J. Comput. Appl. Math. , vol. 230 , pp. 314 – 328 , 2009 .
  • J. M. Zhang , X. Y. Qin , X. Han , and G. Y. Li , A Boundary Face Method for Potential Problems in Three Dimensions , Int. J. Numer. Meth. Eng. , vol. 80 , pp. 320 – 337 , 2009 .
  • S. De , J. Hong , and K. Bathe , On the Method of Finite Spheres in Applications: Towards the Use with ADINA and in a Surgical Simulator , Comput. Mech. , vol. 31 , pp. 27 – 37 , 2003 .
  • J. Hong and K. Bathe , Coupling and Enrichment Schemes for Finite Element and Finite Sphere Discretizations , Comput. Struct. , vol. 83 , pp. 1386 – 1395 , 2005 .
  • Y. Gu and G. Liu , A Boundary Point Interpolation Method for Stress Analysis of Solids , Comput. Mech. , vol. 28 , pp. 47 – 54 , 2002 .
  • J. M. Zhang , Z. H. Yao , and H. Li , A Hybrid Boundary Node Method , Int. J. Numer. Meth. Eng. , vol. 53 , pp. 751 – 763 , 2002 .
  • J. M. Zhang , M. Tanaka , and T. Matsumoto , Meshless Analysis of Potential Problems in Three Dimensions with the Hybrid Boundary Node Method , Int. J. Numer. Meth. Eng. , vol. 59 , pp. 1147 – 1160 , 2004 .
  • J. M. Zhang and Z. H. Yao , Meshless Regular Hybrid Boundary Node Method , CMES: Comput. Model. Eng. Sci. , vol. 2 , pp. 307 – 318 , 2001 .
  • J. M. Zhang and Z. H. Yao , The Meshless Regular Hybrid Boundary Node Method for 2-D Linear Elasticity , Eng. Anal. Bound. Elem. , vol. 27 , pp. 259 – 268 , 2003 .
  • J. M. Zhang and Z. H. Yao , The Regular Hybrid Boundary Node Method for Three-Dimensional Linear Elasticity , Eng. Anal. Bound. Elem. , vol. 28 , pp. 525 – 534 , 2004 .
  • Y. Miao , Y. H. Wang , and F. Yu , Development of Hybrid Boundary Node Method in Two-Dimensional Elasticity , Eng. Anal. Bound. Elem. , vol. 29 , pp. 703 – 712 , 2005 .
  • Y. Miao and Y. H. Wang , Meshless Analysis for Three-Dimensional Elasticity with Singular Hybrid Boundary Node Method , Appl. Math. Mech. , vol. 27 , pp. 673 – 681 , 2006 .
  • Y. Miao , Q. Wang , B. H. Liao , and J. J. Zheng , A Dual Hybrid Boundary Node Method for 2D Elastodynamics Problems , CMES: Comput. Model. Eng. Sci. , vol. 53 , pp. 1 – 22 , 2009 .
  • Y. Miao , Y. Wang , and Y. H. Wang , A Meshless Hybrid Boundary Node Method for Helmholtz Problems , Eng. Anal. Bound. Elem. , vol. 33 , pp. 120 – 127 , 2009 .
  • Q. Wang , J. J. Zheng , Y. Miao , and J. H. Lv , The Multi-domain Hybrid Boundary Node Method for 3D Elasticity , Eng. Anal. Bound. Elem. , vol. 35 , pp. 803 – 810 , 2011 .
  • V. Rokhlin , Rapid Solution of Integral Equations of Classical Potential Theory, J. Comput. Phys. , vol. 60, pp. 187–207, 1985.
  • L. Greengrad and V. Rokhlin , A Fast Algorithm for Particles Simulations , J. Comput. Phys. , vol. 73 , pp. 325 – 348 , 1987 .
  • J. M. Zhang , M. Tanaka , and M. Endo , The Hybrid Boundary Node Method Accelerated by Fast Multipole Expansion Technique for 3D Potential Problems , Int. J. Numer. Meth. Eng. , vol. 63 , pp. 660 – 680 , 2005 .
  • J. M. Zhang and M. Tanaka , Systematic Study of Thermal Properties of CNT Composites by the Fast Multipole Hybrid Boundary Node Method , Eng. Anal. Bound. Elem. , vol. 31 , pp. 388 – 401 , 2007 .
  • J. M. Zhang and M. Tanaka , Fast HDBNM For Large-Scale Thermal Analysis of CNT-Reinforced Composites , Comput. Mech. , vol. 41 , pp. 777 – 787 , 2008 .
  • Q. Wang , Y. Miao , and J. J. Zheng , The Hybrid Boundary Node Method Accelerated by Fast Multipole Expansion Technique for 3D Elasticity , CMES: Comput. Model. Eng. Sci. , vol. 70 , pp. 123 – 151 , 2010 .
  • Q. Wang , Y. Miao , H. P. Zhu , and C. Zhang , An O(N) Fast Multipole Hybrid Boundary Node Method for 3D Elasticity , CMC: Comput. Mater. Con. , vol. 28 , pp. 1 – 25 , 2012 .
  • Q. Wang , Y. Miao , and H. P. Zhu , A Fast Multipole Hybrid Boundary Node Method for Composite Materials , Comput. Mech. , vol. 51 , pp. 885 – 897 , 2013 .
  • S. S. Kulkarni , S. Telukunta , and S. Mukherjee , Application of an Accelerated Boundary-Based Mesh-Free Method to Two-Dimensional Problems in Potential Theory , Comput. Mech. , vol. 32 , pp. 240 – 249 , 2003 .
  • Y. J. Liu , N. Nishimura , and Z. H. Yao , A Fast Multipole Accelerated Method of Fundamental Solutions for Potential Problems , Eng. Anal. Bound. Elem. , vol. 29 , pp. 1016 – 1024 , 2005 .
  • C. A. White and M. Head-Gordon , Fractional Tiers in Fast Multipole Method Calculations , Chem. Phys. Lett. , vol. 257 , pp. 647 – 650 , 1996 .
  • C. A. White and M. Head-Gordon , Rotating Around the Quartic Angular Momentum Barrier in Fast Multipole Method Calculations , J. Chem. Phys. , vol. 105 , pp. 5061 – 5067 , 1996 .
  • L. Greengard and V. Rokhlin , A New Version of the Fast Multipole Method for the Laplace Equation in Three Dimensions , Acta Numer. , vol. 6 , pp. 229 – 269 , 1997 .
  • K. Yoshida , N. Nishimura , and S. Kobayashi , Application of New Fast Multipole Boundary Integral Equation Method to Crack Problems in 3D , Eng. Anal. Bound. Elem. , vol. 25 , pp. 239 – 247 , 2001 .
  • N. Nishimura , Fast Multipole Accelerated Boundary Integral Equation Methods , Appl. Mech. Rev. , vol. 55 , pp. 299 – 324 , 2002 .
  • L. Shen and Y. J. Liu , An Adaptive Fast Multipole Boundary Element Method for Three-Dimensional Potential Problems , Comput. Mech. , vol. 39 , pp. 681 – 691 , 2007 .
  • M. S. Bapat and Y. J. Liu , A New Adaptive Algorithm for the Fast Multipole Boundary Element Method , CMES: Comput. Model. Eng. Sci. , vol. 58 , pp. 161 – 183 , 2010 .
  • J. Zhang and M. Tanaka , Adaptive Spatial Decomposition in Fast Multipole Method , J. Comput. Phys. , vol. 226 , pp. 17 – 28 , 2007 .
  • Y. Saad and M. H. Schultz , GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear System , SIAM J. Sci. Stat. Comput. , vol. 7 , pp. 856 – 869 , 1986 .
  • H. Cheng , L. Greengard , and V. Rokhlin , A Fast Adaptive Multipole Algorithm in Three Dimensions , J. Comput. Phys. , vol. 155 , pp. 468 – 496 , 1999 .
  • Q. Wang , Y. Miao , and H. P. Zhu , A New Formulation for Thermal Analysis of Composites by Hybrid Boundary Node Method , Int. J. Heat. Mass. Transfer , vol. 64 , pp. 322 – 330 , 2013 .

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