PUBLICATIONS:

 

Books

  1.  M.A. Golberg and C.S. Chen, Discrete Projection Methods for Integral Equations, Computational Mechanics Publications, Southampton, Boston, 1997 (425 pages).
  2.   (Editors) C.S. Chen, C.A. Brebbia and D. Pepper, Boundary Element Technology XIII, WIT PRESS, June, 1999.
  3.  (Editors) C.S. Chen, A. Karageorghis, Y.S. Smyrlis, The Method of Fundamental Solutions - A Meshless Method, Dynamic Publishers, 2008.
  4.  C.S. Chen, Y.C. Hon, R.S. Schaback, Scientific Computing with Radial Basis Functions, under review.
  5. Wen Chen, Zhuo-Jia Fu, C.S. Chen, Recent advances on radial basis function collocation methods, 2014, Springer.

Book Chapters

  1. M.A. Golberg and C.S. Chen, The method of fundamental solutions for potential, Helmholtz and diffusion problems, in Boundary Integral Methods - Numerical and Mathematical Aspects, ed. M.A. Golberg, Computational Mechanics Publications, 1998,  pp.103-176.
  2.  C.S. Chen, M.A. Golberg, R.S. Schaback, Recent developments of the dual reciprocity method using compactly supported radial basis functions, in: Transformation of Domain Effects to the Boundary, ed. Y.F. Rashed, WIT PRESS, pp183-225, 2003.  
  3.   C.S. Chen, C.M. Fan, J. Monroe, The method of fundamental solutions for solving elliptic partial differential equations with variable coefficients, in The Method of Fundamental Solutions - A Meshless Method, eds. C.S. Chen, A. Karageorghis, Y.S. Smyrlis, Dynamic Publishers, p. 75-105, 2008.
  4. P.H. Wen, C.S. Chen, Y.W. Liu, Shear deformable plate analysis by the method of fundamental solutions: static and dynamic cases, in The Method of Fundamental Solutions - A Meshless Method, eds. C.S. Chen, A. Karageorghis, Y.S. Smyrlis, Dynamic Publishers, p. 227-246, 2008. 

Referred Journals

 

  1. C.Y. Chan and C.S. Chen, A numerical method for semilinear singular parabolic quenching problems, Quarterly of Applied Mathematics, 47, pp 45-57, 1989.
  2. C.Y. Chan and C.S. Chen, Critical length for global existence of solutions for coupled semilinear singular parabolic problems, Quarterly Applied Mathematics, 47, pp 661-671, 1989.
  3. D. Wan, Peter Shiue and C.S. Chen, Value set of polynomial over finite fields, Proceedings of American Mathematical Society, Vol. 119, No. 3, pp 711 - 717, 1993.
  4. M. Golberg and C. S. Chen, On a method of Atkinson for evaluating domain integrals in the boundary element method, Applied Mathematics and Computation, 60, 1994, pp125-138.
  5. C. S. Chen and A. Muleshkov, Critical lengths for some nonlinear differential equations, Dynamic Systems and Applications, 3, 1994, pp121-134.
  6. M. Golberg and C.S. Chen, The theory of radial basis functions applied to the BEM for inhomogeneous partial differential equations, Boundary Elements Communications, 5, pp 57-61, 1994.
  7. C.S. Chen, The method of fundamental solution for nonlinear thermal explosion, Communications in Numerical Methods in Engineering, 11, pp. 675-681, 1995.
  8. C.S. Chen, The method of fundamental solutions and quasi-monte carlo methods for Possion equation, Lecture Notes in Statistics, 106, pp. 158-167, 1995.
  9. M.A. Golberg, C.S. Chen and S.R. Karur, Improve multiquadric interpolation for partial differential equations, Engineering Analysis with Boundary Elements, 18, 9-17, 1996.
  10. M.A. Golberg and C.S. Chen, A bibliography on radial basis function approximation, Boundary Elements Communications, 7 (4), 155-163, 1996.
  11. M.A. Golberg , C.S. Chen, H. Bowman and H. Power, Some comments on the radial basis functions in the dual reciprocity method, Computational Mechanics, 21, 141-148, 1998.
  12. C.S. Chen and Y.F. Rashed, Evaluation of thin plate spline based particular solution for Helmholtz-type operators for the DRM, Mechanics Research Communications, 25(2), 1998, 195-201.
  13. M. Zerroukat, H. Power and C.S. Chen, A numerical method for heat transfer problem using collocation and radial basis functions, International Journal of Numerical Methods in Engineering, 42, pp. 1263-1278, 1998.
  14. C.S. Chen, M.A. Golberg and Y.C. Hon, Numerical justification of the method of fundamental solutions and the quasi-Monte Carlo method for Poisson-type equations, Engineering Analysis with Boundary Elements, 22, pp. 61-69, 1998.
  15. C.S. Chen, M.A. Golberg and Y.F. Rashed, A mesh free method for linear diffusion equations, Numerical Heat Transfer, Part B, 33, 1998, 469-486.
  16. C.S. Chen, M.A. Golberg and Y.C. Hon, The method of fundamental solutions and quasi-Monte Carlo method for diffusion equations, International Journal of Numerical Methods in Engineering, 43, 1421-1436, 1998.
  17. M.A. Golberg, C.S. Chen and Y.F. Rashed, The annihilator method for computing  particular solutions to partial differential equations, to appear in Engineering Analysis with Boundary Elements, 23, 275-279, 1999.
  18. C.S. Chen, C.A. Brebbia and H. Power, Dual reciprocity method using compactly supported radial basis functions, Communications in Numerical Methods in Engineering, 15, 137-150, 1999.
  19. M.A. Golberg, C.S. Chen and H. Bowman, Some recent results and proposals for the use of radial basis functions in the BEM, Engineering Analysis with Boundary Elements, 23, 285-296, 1999.
  20. A.S. Muleshkov, M.A. Golberg and C.S. Chen, Particular solutions of Helmholtz-type operators using higher order polyharmonic splines, Computational Mechanics, 24, 411-419, 1999.
  21. M.A. Golberg, C.S. Chen and M. Ganesh, Particular solutions of the 3D modified Helmholtz-type equations using compactly supported radial basis functions, Journal of Engineering Analysis with Boundary Elements, vol. 24, pp. 539-547, 2000.
  22. M. Marcozzi, S. Choi and C.S. Chen, On the use of boundary conditions for variational formulations arising in financial mathematics, Journal of Applied Mathematics and Computation, Vol. 124, pp. 197-214, 2001.
  23. M.A. Golberg, C.S. Chen , A mesh free method for solving nonlinear reaction-diffusion equations, the Journal of Computer Modeling in Engineering & Science, 2, pp. 87-96, 2001.
  24. A. D.-H. Cheng, C.S. Chen, M.A. Golberg and Y.F. Rashed, BEM for thermoelasticity and elassticity with body force - a revisit, Engineering Analysis with Boundary Elements, Vol. 25, pp. 377-387, 2001.
  25. Y.F. Rashed, C.S. Chen and M.A. Golberg, Efficient evaluation of plate-half space interaction using contour integrals, Applied Mathematics Modeling, Vol. 25, pp. 967-978, 2001.
  26. Jichun Li and C.S. Chen, A Simple efficient algorithm for interpolation between different grids in both 2D and 3D, Mathematics and Computers in Simulation, Vol. 58(2), pp. 125-132, 2001
  27. C.S. Chen, M.A. Golberg, M. Ganesh, A. H-D. Cheng, Multilevel compact radial functions based computational schemes for some  elliptic problems, Journal of Computers and Mathematics with Application, 43, pp. 359-378, 2002
  28. Xin Li, C.H. Ho and C.S. Chen, Computational test of approximation of functions and their derivatives by radial basis functions, Neural and Parallel in Scientific Computing, 10, pp. 25-46, 2002.
  29. Jichun Li, Y.C. Hon and C.S. Chen, Numerical comparisons of two meshless methods using radial basis functions, Engineering Analysis with Boundary Elements, 26, pp. 205-225, 2002.
  30. M.A. Golberg, A.S. Muleshkov, C.S. Chen, A D.-H. Cheng, Polynomial particular solutions for some partial differential operators, Numerical Methods for Partial Differential Equations, 19, pp. 112-133, 2003.
  31. Jichun Li, A. D.-H. Cheng and C.S. Chen, On the efficiency and exponential convergence of multiquadric collocation methods compared with finite element method, Eng. Anal. with Boundary Elements, 27, pp. 251-257, 2003.
  32. C.S. Chen, G. Kuhn, Jichun Li and G. Mishuris, Radial basis functions for solving near-singular Poisson's Problems, Communication in Numerical Methods in Engineering, 19, pp. 333-347, 2003
  33. Jichun Li and C.S. Chen, Some observations on unsymmetric radial basis functions collocation methods, International Journal of Numerical Methods in Engineering, 57, pp. 1085-1094, 2003
  34. B. Sarler, Janez Perko, C.S. Chen, Radial basis function collocation method solution of natural convection in porous media, International Journal of Numerical Methods for Heat and Fluid Flow, 14(2), pp. 187-212, 2004.
  35. X. Li, C.S. Chen, A mesh free method using Hyperinterpolation and Fast Fourier Transform for solving differential equations, Engineering Analysis with Boundary Elements, 28, pp. 1253-1260, 2004.
  36. 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, International Journal of Numerical Methods in Engineering, 60, pp. 2183-2201, 2004.
  37. C.S. Chen, A.S. Muleshkov, M.A. Golberg, R.M.M. Mattheij, A mesh free approach to solving the axi-symmetric Poisson's equation, Numerical Methods for Partial Differential Equations, 21, pp. 349-367,  2005.
  38. C.J.S. Alves, C.S. Chen, Approximating functions and solutions of non homogeneous partial differential equations using the method of fundamental solutions, Advances in Computational Mathematics, 23, pp. 125-142, 2005.
  39. A.S. Muleshkov, M.A. Golberg, C.S. Chen, Particular solutions for axisymmetric Helmholtz-type operators, Engineering Analysis with Boundary Elements, 29, pp. 1066-1076, 2005.
  40. D. L. Young , T. K. Wong , C. W. Chen , C.M. Fan , C.S. Chen,  Solution of Maxwell's equations by meshless time domain method, CMC, 2, pp. 267-276, 2005
  41. H.A. Cho, C. S. Chen, and M.A. Golberg, Some comments on mitigating the ill-conditioning of the method of fundamental solutions, Engineering Analysis with Boundary Elements, 30, pp. 405-410, 2006.
  42. S.Y. Reutskiy and C.S. Chen, Approximation of multivariate functions and evaluation of particular Solutions using Chebyshev Polynomial and Trigonometric Basis Functions, International Journal in numerical methods in engineering, 67, pp. 1811-1829, 2006.
  43. D. L. Young , C.C. Tsai, Y.C. Lin, C.S. Chen, The Method of Fundamental Solutions for Plate Vibrations, CMC,  4, 1-10, 2006.
  44. C.-S. Huang, S. Wang, C.S. Chen, and Z.-C. Li, A Radial Basis Collocation Method for Hamilton-Jacobi-Bellman Equations, Automatica, 42, 2201-2207, 2006.
  45. Andreas Karageorghis, C.S. Chen, and Y-S Smyrlis, A matrix decomposition method for solving large scale problems using radial basis functions - approximation of functions and their derivatives, Applied Numerical Mathematics, 57, 304-319, 2007.
  46. Radovan Gospavic, Viktor Popov, Milesa Sreckovic, C.S. Chen, DRM-MD approach for modeling laser-material interaction with axial symmetry, Engineering Analysis with Boundary Elements, 31, 200-208, 2007.
  47. C.S. Chen, Sungwook Lee, C.-S. Huang, Derivation of particular solution using chebyshev polynomial based functions, International Journal of Computational Methods, Vol. 4, No. 1, 15-32, 2007
  48. E.V. Glushkov, N.V. Glushkova, C.S. Chen, Semi-analytical solution to heat-transfer problems using Fourier transform technique, radial basis functions and the method of fundamental solutions,  Numerical Heat Transfer, Part B, 52 (5), 409-427, 2007.
  49. Jiu Ding and C.S. Chen, Particular solutions of some elliptic partial differential equations via recursive formulas, Journal of University of Science and Technology of China, 37(11), 1338-1347, 2007.
  50. Sergiy Reutskiy, C.S. Chen, Haiyan Tian, A boundary meshless method using Chebyshev interpolation and trigonometric basis function for solving heat conduction problems, International Journal Numerical Methods in Engineering, 74, 1621-1644, 2008.
  51. Haiyan Tian, Sergiy Reutskiy, C.S. Chen, A basis function for approximation and the solution of partial differential equations, Numerical Methods for Partial Differential Equations, 24, 1018-1036, 2008.
  52. J. Ding, H.Y. Tian, C.S. Chen, The recursive formulation of particular solutions for some elliptic PDEs with polynomial source functions, Communication in Computational Physics, 5, 942-958, 2009.
  53. C.C. Tsai, A. H.-D. Cheng, C.S. Chen, Particular solution of splines and monomials for polyharmonic and products of Helmhlotz operators, Engineering Analysis with Boundary Elements, 33, 514-521, 2009.
  54. C.C. Tsai, C.S. Chen, T.W. Hsu, The method of particular solutions for solving axisymmetric polyharmonic and poly-Helmholtz equations, Engineering Analysis with Boundary Elements, 33, 1396-1402, 2009. 
  55. C.M. Fan, C.S. Chen, J. Monroe, The Method of fundamental Solutions for solving convection-diffusion equations with variable coefficients, Advances in Applied Mathematics and Mechanics, 1, 215-230, 2009.
  56. C.S. Chen, S.Y. Reutskiy, V.Y. Rozov, The method of the fundamental solutions and its modifications for electromagnetic field problems, Computer Assisted Mechanics and Engineering Sciences, 16, 21-33, 2009.
  57. A. Karageorghis, C.S. Chen, and Y.--S. Smyrlis, Matrix decomposition RBF algorithm for solving 3D elliptic problems, Engineering Analysis with Boundary Elements, 33, 1368-1373, 2009.
  58. C.C. Tsai, C.S. Chen, Tai-Wen Hsu, The method of particular solutions for solving axisymmetric polyharmonic  and poly-Helmholtz equation, Engineering Analysis with Boundary Elements, 33, 1396-1402, 2009.
  59. Guangming Yao, C.S. Chen, C.C. Tsai, A Revisit on the derivation of the particular solution for the differential operator \Delta^{2} - \lambda^{2}, Advances in Applied Mathematics and Mechanics, 1, pp. 750-768, 2009.
  60. Ting On Kwok, Leevan Ling, C.S. Chen, Solving 3D inhomogeneous elliptic equations adaptively with the method of particular solutions, International Journal of Computational Methods, 7, 499-511, 2010.
  61. P.H. Wen, C.S. Chen, The method of particular solutions for solving scalar wave equations, International Journal for Numerical Methods in Biomedical Engineering, 26, 1878-1889, 2010.
  62. Ming Li, C.S. Chen, C.H. Tsai, Meshless method based on radial basis functions for solving parabolic partial differential equations with variable coefficients , Numerical Heat Transfer Part BFundamentals, 2010; 57: 333-347.
  63. Ming Li, Y.C. Hon, C.S. Chen, A meshless method for solving nonhomogeneous Cauchy Problems,  Engineering Analysis with Boundary Elements, 35, 499-506, 2011.
  64. Guangming Yao, C.S. Chen, Bozida Sarler, A comparison of three explicit local meshless methods using Radial Basis Functions, Engineering Analysis with Boundary Elements, 35, 600-609, 2011.
  65. C.S. Chen, C.M. Fan, P.H. Wen, The method of particular solutions for solving elliptic problems with variable coefficients, International Journal of Computational Methods, 8, 545-559, 2011.
  66. Guangming Yao, C.S. Chen, Joseph Kolibal, A localized approach for the method of approximate particular solutions, Computers and Mathematics with Applications, 61, 2376-2387, 2011.
  67. A. Tadeu, C.S. Chen, J. Antonio, Nuno Simoes, A boundary meshless method for solving heat transfer problems using Fourier transform, Advances in Applied Mathematics and Mechanics, 3, 572-585, 2011.
  68. C.S. Chen, C.M. Fan, P.H. Wen, The method of particular solutions for solving certain partial differential equations, Numerical Methods for Partial Differential Equations, 28, 506-522, 2012.
  69. Tongsong Jiang, Ming Li, and C.S. Chen, The method of particular solutions for solving inverse problems of a nonhomogeneous convection-diffusion equation with variable coefficients, Numerical Heat Transfer, Part A, 61, 338-352, 2012.
  70. Wen Chen, Ji Lin, C.S. Chen, The method of fundamental solutions for solving exterior axisymmetric Helmholtz problems with high wave number, Advances in Applied Mathematics and Mechanics, 5(4), 477-493, 2013.
  71. C.S. Chen, C-S. Huang, K.H. Lin, On the convergence of the MFS-MPS Scheme for 1D Poisson's Equation, International Journal of Computational Methods, 10(2), 2013. DOI: 10.1142/S0219876213410065
  72. Xingrong Jiang, Wen Chen, C.S. Chen, A fast method of fundamental solutions for solving Helmholtz-type equations, International Journal of Computational Methods, 10(2), 2013. DOI: 10.1142/S0219876213410089.
  73.  Ming Li, Wen Chen, C.S. Chen, A localized RBFs collocation method for solving high dimensional PDEs, Engineering Analysis with Boundary Elements, 37, 1300-1304, 2013.
  74. Xinrong Jiang, Wen Chen, C.S. Chen, Fast multipole accelerated boundary knot method for inhomogeneous Helmholtz problems, Engineering Analysis with Boundary Elements, 37, 1239-1243, 2013.
  75. Ming Li, C.S. Chen, A. Karageorghis, The MFS for the solution of harmonic boundary value problems with non-harmonic boundary conditions, Computers with Mathematics with Applications, 66, 2400-2424, 2013.
  76. Ji Lin, W. Chen, C.S. Chen, X.R. Jiang, Fast boundary knot method for solving axisymmetric Helmholtz problems with high wave number, CMES, 94(6), 485-505, 2013.
  77. Ji Lin, Wen Chen, CS Chen, XR Jiang, Fast boundary knot method for solving axisymmetric Helmholtz problems with high wave-number, CMES: Computer Modeling in Engineering & Sciences,  94( 6), 485-505, 2013.

  1. C.Y. Lin, M.H. Gu, D.L. Young, C.S. Chen, Localized Method of approximate particular solutions with Cole-Hopf transformation for multi-dimensional Burgers equations, Engineering Analysis with Boundary Elements, 40, 78-92, 2014.
  2. Ming Li, C.C. Chu, D.L. Young, C.S. Chen, Transient 3D heat conduction in functionally graded materials by the method of fundamental solution, Engineering Analysis with Boundary Elements, 45, 62-67, 2014.
  3. G. Feng, Ming Li, C.S. Chen, On the ill-conditioning of the method of fundamental solutions for non-harmonic boundary data, Engineering Analysis with Boundary Elements, 41, 98-102, 2014.
  4. Ji Lin, Wen Chen, C.S. Chen, Numerical treatment of acoustic problems with boundary singularities by singular boundary method, Journal of Sound and Vibration, 333, 3177-3188, 2014.
  5. Ming Li, Ghizlane Amazzar, Ahmed Naji, C.S. Chen, Solving Biharmonic equation using the localized method of approximate particular solutions, International Journal of Computer Mathematics, 91(8), 1790-1801, 2014.
  6. Xiao-Yan Liu, Wen Li, Ming Li, C.S. Chen, Circulant matrix and conformal mapping for solving partial differential equations,  Computers and Mathematics with Applications, 68(3), 67-76,2014.
  7. J. Sladek, V. Sladek, S. Krahulec, C.S. Chen, D.L. Young, Analyses of circular magnetoelectroelastic plates with functionally graded material properties, Mechanics of Advanced Materials and Structures,  22, 479-489, 2015.
  8. Wen Li, Ming Li, C.S. Chen, Compactly supported radial basis functions for solving certain high order partial differential equations in 3D, Engineering Analysis with Boundary Elements, 55, 2-9, 2015.
  9. Ji Lin, Wen Chen, C.S. Chen, A new scheme for the solution of reaction diffusion and wave propagation problems, Applied Mathematical Modelling, 38, 5651-5664, 2015.
  10. C.S. Chen, Xingrong Jiang, Wen Chen, Fast solution of the modified Helmholtz equation with the method of fundamental solutions, Communications in Computational Physics, 17(3), 867-886, 2015. 
  11. A.R. Lamichhane, C.S. Chen, The close-form particular solutions for Laplace and biharmonic operators using Gaussian radial basis functions, Applied Mathematics Letters, 46, 50-56, 2015.
  12. Xueying Zhang, C.S. Chen, Local RBFs based collocation methods for unsteady Navier-Stokes equations,  Advances in Applied Mathematics and Mechanics, 7, 430-440, 2015.
  13.  M. Li, C.S. Chen, Y.C. Hon, P.H. Wen, Finite integration method for two-dimensional partial differential equations,  Applied Mathematical Modelling, 39, 4979-4994, 2015. 
  14. G. Yao, Jia Duo, C.S. Chen, L.H. Shen, Implicit local radial basis function interpolations based on function values, Applied Mathematics and Computation, 265,91-102,2015.
  15. C.S. Chen, Guangming Yao, D.L. Young, An improved localized method of approximate particular solutions for solving near singular problems, Computers with Mathematics with Applications, 70, 2883-2894, 2015. 
  16. Xiao-Yan Liu, A. Karageorghis, C.S. Chen, A Kansa-radial basis function method for elliptic boundary value problems in annular domains, Journal of Scientific Computing, 65, 1240-1269, 2015.
  17. Xueing Zhang, Muyuan Chen, C.S. Chen, Zhiyong Li, Local method of approximate particular solutions for solving unsteady Navier-Stokes problem, Applied Mathematical Modelling, 40, 2265-2273, 2016.
  1. Ming Li, Z.L. Tian, Y.C. Hon, C.S. Chen, P.H. Wen, Improved finite integration method for partial differential equations, Engineering Analysis with Boundary Elements, 64,230-2362016.
  2. A.R. Lamichhane, D.L. Young, C.S. Chen, Fast method of approximate particular solutions using Chebyshev interpolation, Engineering Analysis with Boundary Elements, 64, 290-294, 2016.
  3. Ji Lin, C.S. Chen, C.S. Liu, Fast solution of three-dimensional Helmholtz equations by the method of fundamental solutions, Communications in Computational Physics, 20(2), 512-533, 2016.
  1. C.S. Chen, A. Karageorghis, Yan Li, On choosing the location of the sources in the MFS, Numerical Algorithms, 72, 107-130, 2016. 
  2. A. Karageorghis, C.S. Chen, Xiao-Yan Liu, Kansa-RBF algorithms for elliptic problems in axisymmetric domain, SIAM Scientific Computing,  38-1, A471-A499, 2016.
  3. A.R. Lamichhane, C.S. Chen, Particular solution of Matern RBFs and its implementation in the method of particular solutions, International Journal of Computers and Mathematics94(4), 690-706, 2017.
  4.  Thir Dangal, C.S. Chen, Ji Lin, Polynomial particular solutions for solving elliptic partial differential equations,  Computers and Mathematics with Applications, 73(1), 60-70, 2017.
  5. Xiaoyan Liu, C.S. Chen, Andreas Karageorghis, Conformal mapping for the efficient solution of Poisson problems with the Kansa-RBF method, Journal of Scientific Computing, 71(3), 1035-1061, 2017.
  6. Thir Dangal, C.S. Chen, The method of particular solutions for finding the critical domains for the quenching problems, Neural, Parallel, and Scientific Computing, 25, 135-148, 2017.  
  7.  Zhaolu Tian, Zi-Cai Li, Hung-Tsai, C.S. Chen, The method of fundamental solutions for the modified Helmholtz equation, Applied Mathematics and Computation, 305, 262-281, 2017.
  8. Xiangnan Pei, C.S. Chen, Fangfang Dou, The MFS and MAFS for solving Laplace and biharmonic equations, Engineering Analysis with Boundary Element, 80, 87-93, 2017.
  9.  Hui Lv, Fang Hao,  C.S. Chen, The MFS versus the Trefftz method for the Laplace equation in 3D, Engineering Analysis with Boundary Elements, 83, 133-140, 2017.
  10. Andreas Karageorghis, M.A. Jankowska, C.S. Chen, Kansa RBF algorithm for elliptic problems in regular polygonal domain, Numerical Algorithm, 79, 399-421, 2018.
  11. Ji Lin, C.S. Chen, Fajie Wang, Thir Dangal, A new backward node interpolation method using polynomial basis functions for plane bending vibrations, Applied Mathematical Modeling, 49, 452-469, 2017.
  12. Ji Lin, C.S. Chen, Fajie Wang, Thir Dangal, Method of particular solutions using polynomial basis functions for the simulation of plate bending vibrations problems, Applied Mathematical Modelling, 49,452-469, 2017.
  13. M. Jankowska, A. Karageorghis, and C.S. Chen, Kansa RBF method for nonlinear problems, Int. J. comp. Meth. and Exp. Meas., 6(6), 1-8, 2018.
  14. Zhao-Lou Tian, Xingxinang Li, Chia-Ming Fan, C.S. Chen, The method of particular solutions using trigonometric basis functions, Journal of Computational and Applied Mathematics, 335, 20-32, 2018.
  15. M. Jankowska, A. Karageorghis, and C.S. Chen, improved Kansa RBF method for the solution of nonlinear boundary value problems, Engineering Analysis with Boundary Elements 87 173-183, 2018.
  16. Jingang Xiong, Pengfei Jiang, Hui Zheng, C.S. Chen, A high accurate simulation of thin plate problems by using the method of approximate particular solutions with high order polynomial basis, Engineering Analysis with Boundary Elements, 94, 15-158, 2018.
  17. Ji Lin,  A.R. Lamichhane, C.S. Chen, Jun Lu, The adaptive source selection algorithm of the method of fundamental solutions for the solution of harmonic boundary value problems with non-harmonic boundary conditions, Engineering Analysis with Boundary Elements, 95, 154-159, 2018.
  18. Xiao-yan Liu,  C.S. Chen, Wen Li, Ming Li, Particular solutions of products of Helmholtz-type equations using the Matern function, Computers and Mathematics with Applications, 75, 3158-3171, 2018.
  19. Wanru Chang, C.S. Chen, Wen Li, Solving fourth order differential equations using particular solutions of Helmholtz-type equations, American Mathematics Letters, 86, 179-185, 2018.
  20. Fangfang Dou, Zi-Cai Li, C.S. Chen, Zhaolu Tian, Analysis on the method of fundamental solutions for biharmonic equations, Applied Mathematics and Computation, 339, 346-366, 2018.
  21. T.C. Wang, L.H. Shen, D.L. Young, C.S. Chen, Local RBF-DQ method for MHD duct flows at high Hartmann numbers, MOJ Applied Bionics and Biomechanics, 2(1), 71-82, 2018.
  22. Fangfang Dou, Yanshan Liu, C.S. Chen, The method of particular solutions for solving nonlinear Poisson problems, Computers and Mathematics with Applications, 72(2), 501-513, 2019.
  23. C.S. Chen, Andreas Karageorghis, Local Kansa-RBF algorithms for elliptic boundary value problems in annular domain, Communications in Computational Physics, 25, 41-67, 2019.
  24. Dan Wang, C.S. Chen, C.M. Fan, M. Li, The MAPS based on trigonometric basis functions for solving elliptic partial differential equations with variable coefficients and Cauchy-Navier equations, Mathematics and Computers in Simulation, 159, 119-135, 2019
  25. C.M. Fan, Y.K. Huang, C.S. Chen, S.R. Kuo,  Localized method of fundamental solutions for solving two-dimensional Laplace and biharmonic equations, to appear in Engineering Analysis with Boundary Elements, 101, 188-197, 2019.  
  26. B. Khatri Ghimire, Xinxiang Li, C.S. Chen,  A.R. Lamichhane, Hybrid Chebyshev Polynomial Scheme for Solving Elliptic Partial Differential Equations, Journal of Computational and Applied Mathematics, 364, 112324, 2020.


  27. D.W. Watson, A. Karageorghis, C.S. Chen, The radial basis function-differential quadrature method for elliptic problems in annular domains, Journal of Computational and Applied Mathematics, 363, 53-76, 2020. 
  28. Dan Wang, C.S. Chen, Wen Li, An efficien MAPS for solving fourth order partial differential equations using trigonometric functions, Computers and Mathematics with Applications, 79, 934-946, 2020.
  29. Ji Lin, Sergiy Reutskiy, C.S. Chen, Jun Lu, A novel method for solving time-dependent 2D advection-diffusion-reaction equations to model transfer in nnlinear anisotropic media, Communications in Computational Physics,  173, 105-114, 2020.
  30. Wanru Chang, C.S. Chen, Xio-Yan Liu, Ming Li, Localized meshless method based on polynomial basis functions for solving axisymmetric equations, Mathematics and Computers in Simulation, 177, 487-499, 2020
  31. Cheng Deng, Hui Zheng, Mingfu Fu, Jingang Xiong, C.S. Chen, An efficient method of approximate particular solutions using polynomial basis functions, Engineering Analysis with Boundary Elements, 111, 1-8, 2020.
  32. Cheng Deng, Yan Shi, Hui Zheng, C.S. Chen, Solving fourth-order PDEs using the LMAPS, Advances in Applied Mathematics and Mechanics, 12, 920-939, 2020.
  33. C.S. Chen, Andreas Karageorghis, Hui Zheng, Radial basis function collocation methods for fourth order boundary value problems, Communication in Computational Physics, 27, 1530-1549, 2020.
  34. Xiao-yan Liu, Hui Wang, C.S. Chen, Qing Wang, Ming Li, Yong Wang, Implicit surface reconstruction with radial basis functions via PDEs, Engineering Analysis with Boundary Elements, 110, 95-103, 2020.
  35. C.S. Chen, Shu-Hui Shen, Fangfang Dou, LMAPS for solving four-order PDEs with polynomial basis functions, Mathematics and Computers in Simulation, 177, 500-515, 2020.
  36. Q. Xi, C.S. Chen, Zhou-Jia Fu, Eva Comino, The MAPS with polynomial basis functions for solving axisymmetric time-fractional equations, Computers and Mathematics with Applications, 88, 78-90, 2021.


  37. Hui Zheng, C.S. Chen, M. Lei, Yang Wang, Improved 3D surface reconstruction based on  the method of fundamental solutions, Numer. Math. Theor. Meth. Appl., 13, 973-985, 2020
  38. C.S. Chen, Andreas Karageorghis, Hui Zheng, Improved RBF collocation methods for fourth order boundary value problems, Communication in Computational Physics, 27, 1530-1549, 2020.
  39. Yanhua Cao, C.S. Chen, Hui Zheng, Space-time polynomial particular solution method for solving time-dependent problems, Numerical Heat Transfer (Part B), 77, 181-194, 2020.
  40. C.S. Chen, Andreas Karageorghis, Fangfang Dou, A novel RBF collocation method using fictitious centers, Applied Mathematics Letters, 101, 106069, 2020.
  41. Xiaomin Zhu, Fangfang Dou, Andreas Karageorghis, C.S. Chen, A fictitious points one-step MPS-MFS technique, Applied Mathematics and Computation, 382, 2020, 125332. 
  42. Andreas Karageorghis Demetriana Tappoura, C.S. Chen, Kansa RBF method with auxiliary boundary cetres for fourth order BVPs, Mathematics and Computers in Simulation, 181, 581-597, 2020.
  43. Fangfang Dou,  Li-Ping Zhang, Zi-Cai Li, C. S. Chen, Source Nodes on Elliptic  Pseudo-boundaries in  Method of Fundamental Solutions for Laplace's Equation; Selection of  Pseudo-boundaries, Journal of Computational and Applied Mathematics, 377, 112861, 2020.
  44. Ji Lin, Yuxiang Zhao, Daniel Watson, C.S. Chen, The radial basis function differential quadrature method with ghost points, Mathematics and Computers in Simulation, 173, 105-114, 2020.
  45. Z.Y. Ma, X.X. Li, C.S. Chen, Ghost point method using RBFs and polynomial basis functions, Applied Mathematics Letters, 111, 106618, 2021.
  46. Zhuo-Chao Tang, C.S. Chen, Zhou-Jia Fu, A localized MAPS using polynomial basis functions for the fourth order concave-shape plate bending equations, Archive of Applied Mechanics, 90(10), 2241-2253, 2021. 
  47. C.S. Chen, Malgorzata A. Jankowska, Andreas Karageorghis, RBF-DQ algorithms for elliptic problems in axisymmetric domains, Numerical Algorithms, 2021. online https://doi.org/10.1007/s11075-021-01105-w
  48. D.L. Young, Shin-Ruei Lin, Chuin-Shan Chen, C.S. Chen, Two--step MPS--MFS ghost point method for solving partial differential equations, Computers and Mathematics with Applications, 94, 38-46, 2021.
  49. C.S. Chen, Lionel Amuzu, Kwesi Acheampong, Huiqing Zhu, Improved geometric modeling using the method of fundamental solutions, Engineering Analysis with Boundary Elements, 130, 49-57, 2021.
  50. C.S. Chen, A. Karageorghis, Lionel Amuzu, Kansa RBF method with auxiliary boundary centres for high order BVP, to appear in Journal of Computational and Applied Mathematics, 398, 113680, 2021.   https://doi.org/10.1016/j.cam.2021.113680.


  51. Hui Zheng,  Zhuowan Fan, Jichun Li, C.S. Chen, A meshfree RBR collocation method for negative reflections of electromagetic wave propagation in metamaterials, submitted.


    Refereed Conference Proceeding

     

    1.      C.Y. Chan and C. S. Chen, A nonlinear singular parabolic initial boundary value problem, ed. V. Lakshmikantham, Nonlinear Analysis and Applications, Marcel Dekker, New York, 1987, pp 115-119.

    2.      A. Muleshkov and C.S. Chen, A note on the critical length for mixed boundary value problems,  Proceedings of the First International Conference on Dynamic System and Applications, 1, 271-276, 1994.

    3.      C.S. Chen and M. Golberg, A domain embedding method and the quasi-monte carlo method for Poisson's Equation, Boundary Elements XVII, Computational Mechanics Publications, Boston, Southampton, 1995, 115-122.

    4.      C.Y. Chan and C.S. Chen, Method of fundamental solutions for multi-dimensional quenching problems, Proceeding of Dynamic Systems and Applications, 2, ed. G.S. Ladde and M. Sambandham, 1996, 115-121.

    5.      C.S. Chen and M.A. Golberg, Las Vegas method for diffusion equations, Boundary Element Technology XII, eds. J.I. Frankel, C.A. Brebbia & M.A.H. Aliabadi, Computational Mechanics Publications, 1997, 299-308.

    6.      C.S. Chen and C.A. Brebbia, The dual reciprocity method for Helmholtz-type operators, Boundary Element Method XX, eds. A. Kassab, C.A. Brebbia, M. Chopra, Computationa Mechanics Publications, 1998, 495-504.

    7.      M. Marcozzi, S. Choi and C.S. Chen, RBF and optimal stopping problems; an application to the pricing of Vanilla options on one risky asset, Boundary Element Technology XIII, eds. C.S. Chen, C.A. Brebbia, D.W. Pepper, WIT Press, Boston, Southampton, pp. 345-354, 1999.

    8.      C.S. Chen, M. Marcozzi and S. Choi, The method of fundamental solutions and compactly supported radial basis functions - a meshless approach to 3D problems, Boundary Element Methods XXI, eds. C.A. Brebbia, H. Power, WIT Press, Boston, Southampton, pp. 561-570, 1999.

    9.      C.S. Chen, A.S. Muleshkov and M.A. Golberg, The numerical evaluation of particular solutions for Poisson's equation - a revisit, Boundary Element Methods XXI, eds. C.A. Brebbia, H. Power, WIT Press, Boston, Southampton, pp. 313-322, 1999.

    10.  M.A. Golberg, C.S. Chen & A.S. Muleshkov, The method of fundamental solutions for diffusion equations, Boundary Element Technology XIII, eds. C.S. Chen, C.A. Brebbia, D.W. Pepper, WIT Press, Boston, Southampton, pp. 377-386, 1999.

    11.  Y.F. Rashed, C.S. Chen and M.A. Golberg, Equivalent boundary integrals for Boussinesq - Cerruti half interaction with thin plates, Boundary Element Methods XXI, eds. C.A. Brebbia, H. Power, WIT Press, Boston, Southampton, pp. 615-625, 1999. 

    12.  A.H.-D. Cheng, C.S. Chen, M.A. Golberg and D.-L. Young, Radial basis functions, polynomial basis functions, particular solutions and DRBEM, 14th Engineering Mechanics Conference, Austin, Texas, May 21-24, 2000 (in CD ROM).

    13.  C.S. Chen, M.A. Golberg, M. Ganesh, A. H-D. Cheng, The dual reciprocity method using multilevel method compactly supported radial basis functions, Boundary Element Methods XXII, eds. C.A. Brebbia, H. Power, WIT Press, Boston, Southampton, pp. 555-564, 2000

    14.  A.S. Muleshkov, C.S. Chen, M.A. Golberg and A.H-D. Cheng, Analytic particular solutions for inhomogeneous Helmholtz-type equations, Advances in Computational Engineering & Sciences, eds. S.N. Atluri, F.W. Brust, Tech Science Press, Vol. 1, pp. 27-32, 2000.

    15.  M.A. Golberg, C.S. Chen and V. Popov, A mesh free method for nonlinear reaction-diffusion equation, Advances in Computational Engineering & Sciences, eds. S.N. Atluri, F.W. Brust, Tech Science Press, Vol. 1, pp. 2-7, 2000

    16.  J. Jerko, C.S. Chen, B. Sarler, A polygone-free to steady natural convection in solid-liquid systems, Moving Boundaries VI, ed. B. Sarler and C.A. Brebbia, WIT Press, Southampton, pp. 112-122, 2001

    17.  Xin Li, C.H. Ho and C.S. Chen, Computational test of approximation of functions and their derivatives by radial basis functions, Advances in Computational Engineering & Sciences, eds. S.N. Atluri, T. Nishioka, M. Kikuchi, Tech Science Press, Los Angels, CD-ROM, # 76, 2001. 

    18.  M. Ludian, Jichun Li and C.S. Chen, The DRM using Helmholtz-type operators, Advances in Computational Engineering & Sciences, eds. S.N. Atluri, T. Nishioka, M. Kikuchi, Tech Science Press, Los Angels, CD-ROM, # 77, 2001. 

    19.  C.J.S. Alves, C.S. Chen, The MFS method adapted for a non homogeneous equation, Advances in Computational Engineering & Sciences, eds. S.N. Atluri, T. Nishioka, M. Kikuchi, Tech Science Press, Los Angels, CD-ROM, # 135, 2001

    20.  B. Sarler, J. Perko and C.S. Chen, A meshless approach for natural convection, Advances in Computational Engineering & Sciences, eds. S.N. Atluri, T. Nishioka, M. Kikuchi, Tech Science Press, Los Angels, CD-ROM, # 150, 2001.

    21.  C.J.S. Alves, C.S. Chen and B. Sarler, The method of fundamental solutions for solving Poisson problems, Boundary Elements XXIV, eds. C.A. Brebbia, A. Tadeu and V. Popov, WIT Press, Southampton, Boston, pp. 67-76, 2002.

    22.  A.S. Muleshkov, M.A. Golberg, A.H-D. Cheng and  C.S. Chen, Polynomial particular solutions for Poisson problems, Boundary Elements XXIV, eds. C.A. Brebbia, A. Tadeu and V. Popov, WIT Press, Southampton, Boston, pp. 115-124, 2002.

    23.  J. Li, C.S. Chen, D. Pepper and Y. Chen, Mesh-free method for groundwater modeling, Boundary Elements XXIV, eds. C.A. Brebbia, A. Tadeu and V. Popov, WIT Press, Southampton, Boston, pp. 145-154, 2002.

    24.   D.W. Pepper, C.S. Chen , A meshless method for modeling heat transfer, Advances in Computational Engineering & Sciences, eds. S.N. Atluri, D.W. Pepper, Tech Science Press, Los Angels, #156, 2002.

    25.  B. Sarler, R. Vertnik; M. Savic, C.S. Chen, A meshless approach for hallow-brick temperature field, Advances in Computational Engineering & Sciences, eds. S.N. Atluri, D.W. Pepper, Tech Science Press, Los Angels, #154, 2002.

    26.   B. Sarler, J. Perko and C.S. Chen, Natural convection in Porous Media -radial basis function collocation method solution of the Darcy model, to appear in Fifth World Congress on Computational Mechanics, 2002.

    27.  D.W. Pepper, C.S. Chen and Jichun Li, Modeling heat transfer using adaptive finite elements, boundary elements, and meshless methods, in Advanced Computational Methods in Heat Transfer, eds. B. Sunden and C.A. Brebbia, WIT Press, Southampton, Boston, 2002.

    28.  Jichun Li, A. D.-H. Cheng and C.S. Chen, On the efficiency and exponential convergence of multiquadric collocation methods compared with finite element method, Eng. Anal. with Boundary Elements, 27, pp. 251-257, 2003.

    29.  M. S. Ingber and C. S, Chen, A parallel domain decomposition approach for solving diffusion equations using the method of fundamental solutions, in Proceedings of the 6th ASME-JSME Thermal Engineering Joint Conference, AJTEC2003, Hawaii Island, Hawaii, Japan Society of Mechanical Engineers (2003).

    30.  A.S. Muleshkov, M.A. Golberg, C.S. Chen, The method of fundamental solutions for solving the axisymmetric Poisson equation, Advances in Computational & Experimental Engineering & Sciences, eds. S.N. Atluri, D.E. Beskos; D. Polyzos, 2003.

    31.  Xin Li, C.S. Chen, Computation of particular solutions by Hyperinterpolation and Fast Fourier Transform, Advances in Computational & Experimental Engineering & Sciences, eds. S.N. Atluri,, D.E. Beskos; D. Polyzos, 2003, CD-ROM.

    32.  B. Sarler, I. Kovacevic, and C.S. Chen, A mesh-free solution of temperature in direct-chill cast slabs and billets. V: MAMMOLI, A.A. (ed.), BREBBIA, Carlos Alberto (ed.). Moving boundaries VII computational modeling of free and moving boundary problems, (Computational and experimental methods, vol. 10). Southampton, Boston: WIT Press, 2003, pp.271-280.

    33.  Valjean Elander, C. S. Chen, Darrell Pepper, The Method of Fundamental Solutions for Axi-symmetric Problems, 2003 ASME Summer Heat Transfer Conference Proceeding, CD ROM.

    34.  A. Tadeu, L. Godinho, C. S. Chen, Performance of the BEM, MFS, and RBF Collocation Method in a 2.5D wave propagation analysis, Boundary Elements XXVII, eds. A. Kassab, C.A. Brebbia, E. Divo, and D. Poljak, p.143-153, 2005.

    35.  B. Sarler, T. Tran-Cong, C.S. Chen, Meshfree direct and indirect local radial basis function collocation formulations for transport phenomena, Boundary Elements XXVII, eds. A. Kassab, C.A. Brebbia, E. Divo, and D. Poljak, p.417-427, 2005.

    36.  J. Li, C.S. Chen, Y.C. Hon, Radial basis meshless methods for unsaturated flow problems, Boundary Elements XXVII, eds. A. Kassab, C.A. Brebbia, E. Divo, and D. Poljak, p.25-35, 2005.

    37.  B. Sarler, Janez Perko, C.S. Chen, Numerical Diffusion of Meshless Diffuse Approximate Method, International Conference on Computational & Experimental Engineering, CD-ROM, 2006.

    38.  H.Y. Tian, S. Reutskiy, and C.S. Chen, New basis functions and their applications to PDEs, Proceedings of International Conference on Computational & Experimental Engineering and Sciences, 851-857, 2007.

    39.  R. Gospavic, N. Haque, V. Popov, C.S. Chen, Comparison of two solvers for the extended method of fundamental solutions,  Boundary Elements and Other Meshless Reduction Method XXX, eds. P. Skerget and C.A. Brebbia, p. 191-199, 2008.

    40.  Guangming Yao, C.S. Chen, Marina Jelen, Bozidar Sarler,  Meshless solutions of temperature fields for use in dendritic growth simulations, Proceedings of the International Conference on Optimization using Exergy-Based Methods and Computational Fluid Dynamics, Berlin, Germany, October 20-23, 2009.

    41.  Wataru Fujisaki, C.S. Chen, Suitable allocation of collocation/sources for notched plate problems by the MFS, Proceeding of Computational Engineering Conference, Vol. 19, 2014.

    42.  A. Karageorghis, C.S. Chen, A Kansa-RBF method for Poisson problems in annular domain, Proceeding of BEM/MRM 37, 2014.

    43.  Ji Lin, Wen Chen, C.S. Chen, Fast evaluation of the method of fundamental solutions for solving reaction diffusion problems, Conference Proceeding of Third International Conference on Computational Methods for Thermal Problems, THERMACOMP2014, editors: B. Sarler, N. Massarotti, P. Nithiarasu, p. 263-266, 2014.

    44.  Xiao-Yan Liu, Wen Li and C.S. Chen, Fast matrix decomposition method for solving Poisson problems, Conference Proceeding of International Conference on Computational Methods for Thermal Problems, THERMACOMP2014, editors: B. Sarler, N. Massarotti, P. Nithiarasu, p. 275-278, 2014.

    45.  P.H. Wen, C.S. Chen, Y.C. Hon, M. Li, Finite integration method for solving multi-dimensional partial differential equations, ICCM 2014.