SemiAnalytical Solution to Heat Transfer Problems Using Fourier Transform Technique, Radial Basis Functions, and the Method of Fundamental Solutions

REFERENCES

• G. L. Moridis and D. L. Reddell , The Laplace Transform Boundary Element (LTBE) Method for the Solution of Diffusion-Type Equations , Boundary Elements XIII , vol. 1 , pp. 83 – 97 , Springer–Verlag , Berlin , 1991 .
   Google Scholar
• C. K. Chen , T. M. Chen , and J. W. Cleaver , New Hybrid Laplace Transform/Finite Element Method for Two-Dimensional Transient Heat Conduction Problem , Numer. Heat Transfer B , vol. 20 , pp. 191 – 205 , 1991 .
   Web of Science ®Google Scholar
• S. Zhu , P. Satravaha , and X. Lu , Solving Linear Diffusion Equations with the Dual Reciprocity Method in Laplace Space , Eng. Anal. Boundary Elem. , vol. 13 , pp. 1 – 10 , 1994 .
   Web of Science ®Google Scholar
• C. S. Chen , M. A. Golberg , and Y. F. Rashed , A Mesh Free Method for Linear Diffusion Equations , Numer. Heat Transfer B , vol. 33 , pp. 469 – 486 , 1998 .
   Web of Science ®Google Scholar
• M. A. Golberg and C. S. Chen , A Mesh Free Method for Solving Nonlinear Reaction-Diffusion Equations , J. Comput. Model. Eng. Sci. , vol. 2 , pp. 87 – 95 , 2001 .
   Google Scholar
• M. S. Ingber , C. S. Chen , and J. A. Tanski , A Mesh Free Approach Using Radial Basis Functions and Parallel Domain Decomposition for Solving Three Dimensional Diffusion Equations , Int. J. Numer. Meth. Eng. , vol. 60 , pp. 2183 – 2201 , 2004 .
   Web of Science ®Google Scholar
• X. Li and C. S. Chen , A Mesh-Free Method Using Hyperinterpolation and Fast Fourier Transform for Solving Differential Equation , Eng. Anal. Boundary Elem. , vol. 28 , pp. 1253 – 1260 , 2004 .
   Google Scholar
• Y. Liu , X. Zhang , and M. W. Lu , A Meshless Method Based on Least Squares Approach for Steady- and Unsteady-State Heat Conduction Problems , Numer. Heat Transfer B , vol. 47 , pp. 257 – 275 , 2005 .
   Web of Science ®Google Scholar
• H. Sadat , N. Dubus , L. Gbahoué and T. Sophy , On the Solution of Heterogeneous Heat Conduction Problems by a Diffuse Approximation Meshless Method , Numer. Heat Transfer B , 50 , pp. 491 – 498 , 2006 .
   Web of Science ®Google Scholar
• R. M. Cotta and J. E. V. Gerk , Mixed Finite-Difference/Integral Transform Approach for Parabolic-Hyperbolic Problems in Transient Forced Convection, Numer. Heat Transfer B , vol. 25, pp. 433–448, 1994.
   Web of Science ®Google Scholar
• Der-Liang Young , Chia-Cheng Tsai , and Chia-Ming Fan , Direct Approach to Solve Nonhomogeneous Diffusion Problems Using Fundamental Solutions and Dual Reciprocity Methods , J. Chin. Inst. Eng. , vol. 27 , pp. 597 – 609 , 2004 .
   Web of Science ®Google Scholar
• H. Cho , M. A. Golberg , A. S. Muleshkov , and X. Li , Trefftz Methods for Time Dependent Partial Differential Equations , Journal of Computers, Materials and Continua , vol. 1 , pp. 1 – 37 , 2004 .
   Web of Science ®Google Scholar
• G. Fairweather and A. Karageorghis , The Method of Fundamental Solution for Elliptic Boundary Value Problems , Adv. Comput. Math. , vol. 9 , pp. 69 – 95 , 1998 .
   Web of Science ®Google Scholar
• M. A. Golberg and C. S. Chen , The Method of Fundamental Solutions for Potential, Helmholtz and Diffusion Problems , in M. A. Golberg (ed.), Boundary Integral Methods—Numerical and Mathematical Aspects , pp. 103 – 176 , Computational Mechanics Publications , Southampton , England , 1998 .
   Google Scholar
• K. E. Atkinson , The Numerical Evaluation of Particular Solutions for Poisson's Equation , IMA J. Numer. Anal. , vol. 5 , pp. 319 – 338 , 1985 .
   Google Scholar
• A. S. Muleshkov , M. A. Golberg , and C. S. Chen , Particular Solutions of Helmholtz-Type Operators Using Higher Order Polyharmonic Splines , Comput. Mech. , vol. 23 , pp. 411 – 419 , 1999 .
   Google Scholar
• C. S. Chen , M. A. Golberg , and R. S. Schaback , Recent Developments of the Dual Reciprocity Method Using Compactly Supported Radial Basis Functions , in Y. F. Rashed (ed.), Transformation of Domain Effects to the Boundary , pp. 183 – 225 , WIT Press , Southampton , England , 2003 .
   Google Scholar
• P. W. Partridge , C. A. Brebbia , and L. C. Wrobel , The Dual Reciprocity Boundary Element Method , Computational Mechanics Publications , Southampton , England , 1992 .
   Google Scholar
• E. Glushkov and N. Glushkova , On the Efficient Implementation of the Integral Equation Method in Elastodynamics , J. Computat. Acoustics , vol. 9 , pp. 889 – 898 , 2001 .
   Google Scholar
• M. Abramowitz and I. A. Stegun (eds.), Handbook of Mathematical Functions , Applied Mathematics Series 55, National Bureau of Standards , Washington , DC , 1964 .
   Google Scholar
• V. A. Babeshko , E. V. Glushkov , and J. F. Zinchenko , Dynamics of Inhomogeneous Linearly Elastic Media , pp. 1 – 344 , Nauka , Moscow , 1989 (in Russian) .
   Google Scholar
• H. Bateman and A. Erdelyi , Higher Transcendental Functions , vol. 2 , McGraw-Hill , New York , 1953 .
   Google Scholar
• J. E. Marsden , Basic Complex Analysis , W. H. Freeman & Company , 1973 .
   Google Scholar
• A. Tadeu , C. S. Chen , J. Antonio , and Nuno Simoes , Conduction Heat Transfer under Nonzero Initial Conditions: A Solution Using the Method of Particular Solutions in the Frequency Domain, submitted , 2007 .
   Google Scholar
• H. Akima , A New Method of Interpolation and Smooth Curve Fitting Based on Local Procedures , J. ACM , vol. 17 , pp. 589 – 602 , 1970 .
   Web of Science ®Google Scholar