References
- P.M. Anselone, Collectively Compact Operator Approximation Theory, Prentice-Hall, Englewood Cliffs, NJ, 1971.
- P.M. Anselone, Singularity subtraction in numerical solution of integral equations, J. Aust. Math. Soc. 22 (1981), pp. 408–418. doi: 10.1017/S0334270000002757
- P.M. Anselone and T.W. Palmer, Collectively compact sets of linear operators, Pacific J. Math. 25 (1968), pp. 417–422. doi: 10.2140/pjm.1968.25.417
- P.M. Anselone and M.L. Treuden, Regular operator approximation theory, Pacific J. Math. 120 (1985), pp. 257–268. doi: 10.2140/pjm.1985.120.257
- K. Atkinson, The Numerical Solution of Integral Equations of the Second Kind, Cambridge University Press, Cambridge, 1997.
- P.K. Banerjee and R. Butterfield, Boundary Element Methods in Engineering Science, McGraw Hill, Maidenhead, 1981.
- Y.P. Chang, C.S. Kang, and D.J. Chen, The use of fundamental Green's functions for the solution of heat conduction in anisotropic media, Int. J. Heat Mass. Transf. 16 (1973), pp. 1905–1908. doi: 10.1016/0017-9310(73)90208-1
- F. Chatelin, Spectral Approximation of Linear Operator, Academic Press, New York, 1983.
- M. Costabel, V.J. Ervin, and E.P. Stephan, On the convergence of collocation methods for Symm's integral equation on open curves, Math. Comp. 51 (1988), pp. 167–179.
- D. David, Sigmoidal transformations and the trapezoidal rule, J. Aust. Math. Soc. B 40 (1998), pp. 77–137.
- P. Davis, Circulant Matrices, John Wiley and Sons, New York, 1979.
- P. Davis, Methods of Numerical Integration, 2nd ed., Academic Press, New York, 1984.
- J. Huang and T. Lü, The mechanical quadrature methods and their extrapolation for solving BIE of Steklov eigenvalue problems, J. Comput. Math. 22 (2004), pp. 719–726.
- J. Huang and Z. Wang, Extrapolation algorithms for solving mixed boundary integral equations of the Helmholtz equation by mechanical quadrature methods, SIAM J. Sci. Comput. 31 (2009), pp. 4115–4129. doi: 10.1137/080740763
- J. Huang, H.-T. Huang, Z.-C. Li, and Y.M. Wei, Stability analysis via condition number and effective condition number for the first kind boundary integral equations by advanced quadrature methods, a comparison, Eng. Anal. Bound. Elem. 25 (2010), pp. 115–128.
- J. Huang, Z.-C. Li, I.-L. Chen, and H.D.C. Alexander, Advanced quadrature methods and splitting extrapolation algorithms for first kind boundary integral equations of Laplace's equation with discontinuity solutions, Eng. Anal. Bound. Elem. 34 (2010), pp. 1003–1008. doi: 10.1016/j.enganabound.2010.07.004
- J. Huang, G. Zeng, X.-M. He, and Z.-C. Li, Splitting extrapolation algorithm for first kind boundary integral equations with singularities by mechanical quadrature methods, Adv. Comput. Math. 36 (2012), pp. 79–97. doi: 10.1007/s10444-011-9181-8
- R. Kress, Linear Integral Equations, Springer-Verlag, Berlin, 1989.
- W.H. Li, Fluid Mechanics in Water Resources Engineering, Allyn and Bacon, Toronto, 1983.
- N.S. Mera, L. Elliott, D.B. Ingham, and D. Lesnic, An iterative bem for the cauchy steady state heat conduction problem in an anisotropic medium with unknown thermal conductivity tensor, Inv. Probl. Eng. 8 (2000), pp. 579–607. doi: 10.1080/174159700088027748
- N.S. Mera, L. Elliott, D.B. Ingham, and D. Lesnic, A comparison of boundary element method formulations for steady state anisotropic heat conduction problems, Eng. Anal. Bound. Elem. 25 (2001), pp. 115–128. doi: 10.1016/S0955-7997(00)00050-3
- J. Saranen, The modified quadrature method for logarithmic-kernel integral equations on closed curves, J. Int. Equ. Appl. 3 (1991), pp. 575–600. doi: 10.1216/jiea/1181075650
- J. Saranen and I. Sloan, Quadrature methods for logarithmic-kernel integral equations on closed curves, IMA J. Numer. Anal. 12 (1992), pp. 167–187. doi: 10.1093/imanum/12.2.167
- L.J. Segerlind, Applied Finite Element Analysis, John Wiley, New York, 1984.
- Y.C. Shiah and C.L. Tan, BEM treatment of two-dimensional anisotropic field problems by direct domain mapping, Eng. Anal. Bound. Elem. 20 (1997), pp. 347–351. doi: 10.1016/S0955-7997(97)00103-3
- A. Sidi, A new variable transformation for numerical integration, Int. Ser. Numer. Math. 112 (1993), pp. 359–373.
- A. Sidi, Exitension of a class of periodizing variable transformations for numerical integration, Math. Comp. 75 (2005), pp. 327–343. doi: 10.1090/S0025-5718-05-01773-4
- A. Sidi and M. Israeli, Quadrature methods for periodic singular and weakly singular Fredholm integral equation, J. Sci. Comput. 3 (1988), pp. 201–231. doi: 10.1007/BF01061258
- I.H. Sloan and A. Spence, The Galerkin method for integral equations of first-kind with logarithmic kernel: theory, IMA J. Numer. Anal. 8 (1988), pp. 105–122. doi: 10.1093/imanum/8.1.105
- E.P. Stephan and W.L. Wendland, An augmented Galerkin procedure for the boundary integral method applied to two-dimensional screen and crack problems, Appl. Anal. 18 (1984), pp. 183–219. doi: 10.1080/00036818408839520
- Y. Yan, The collocation method for first-kind boundary integral equations on polygonal regions, Math. Comp. 54 (1990), pp. 139–154. doi: 10.1090/S0025-5718-1990-0995213-6
- Y. Yan and I. Sloan, On integral equations of the first kind with logarithmic kernels, J. Int. Equ. Appl. 1 (1988), pp. 517–548. doi: 10.1216/JIE-1988-1-4-517
- J.-J. Zhang, C.L. Tan, and F.F. Afagh, A general exact transformation of body-force volume integral in BEM for 2D anisotropic elasticity, Comput. Mech. 19 (1996), pp. 1–10. doi: 10.1007/BF02757779
- O.C. Zienkiewicz, The Finite Element Method, McGraw Hill, Maidenhead, 1977.