**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**32131

##### High Accuracy Eigensolutions in Elasticity for Boundary Integral Equations by Nyström Method

**Authors:**
Pan Cheng,
Jin Huang,
Guang Zeng

**Abstract:**

**Keywords:**
boundary integral equation,
extrapolation algorithm,
aposteriori error estimate,
elasticity.

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1070723

**References:**

[1] A.R.Hadjesfandiari, G.F.Dargush, Boundary eigensolutions in elasticity 1: theoretical development, J.Solids Structure, 38(2001), 6589-6625.

[2] P.K.Banerjee, The boundary element methods in engineering, McGraw- Hill, London, 1994.

[3] Y.Z.Chen, Z.X.Wang, X.Y.Lin, Eigenvalue and eigenfunction analysis arising from degenerate scale problem of BIE in plane elasticity, Eng.Anal.Bound. Element, 31(2007), 994-1002.

[4] P.M.Anselone, Singularity subtraction in the numerical solution of integral equations, J.Austral.Math.Soc. (Series B), 22(1981), 408-418.

[5] C.A.Brebbia, S.Walker, Boundary elements techniques in engineering, Butter worth and Co., Boston, 1980.

[6] M.Willian, Strongly elliptic systems and boundary integral equations, Cambridge University Press, 2000.

[7] G.H.Paulino, G.Menom, S.Mukherjee, Error estimation using hypersingular integrals in boundary element methods for linear elasticity, Engineering Analysis with Boundary Elements, 25(2001), 523-534.

[8] V.Z.Parton, P.I.Perlin, Integral equations in elasticity, Mir Publishers, Moscow, 1977.

[9] A.R.Hadjesfandiari, G.F.Dargush, Boundary eigensolutions in elasticity II. Application to computational mechanics, J.Solids Structure, 40(2003), 1001-1031.

[10] A.R.Hadjesfandiari, G.F.Dargush, Computational mechanics based on the theory of boundary eigensolutions, Int.J.Numer.Mech.Eng., 50(2001), 325-346.

[11] G.Cohen, S.Fauqueux, Mixed spectral finite elements for the linear elasticity system in unbounded domains, SIAM J.Numer.Anal., 3(2005), 864-884.

[12] L.F.Pavarino, Preconditioned mixed spectral element methods for elasticity and stokes problems, SIAM J. Sci. Comput., 6(1998), 1941-1957.

[13] C.J.Talbot, A.Crampton, Application of the pseudo-spectral method to 2D eigenvalue problems in elasticity, Numer.Algortihms, 38(2005), 95C110.

[14] Z.Cai, T.A.Manteuffel, S.F.Mccormick, First-order system least squares for the stokes equations with application to linear elasticity, SIAM J.Numer.Anal., 5(1997), 1727-1741.

[15] Z.Cai, G.Starke, Least-squares methods for linear elasticity , SIAM J. Numer. Anal., 2(2004), 826-842.

[16] J.Huang, T.L┬¿u, The mechanical quadrature methods and their extrapolation for solving BIE of Steklov eigenvalue problems, J. Comp. Math., 5(2004), 719-726

[17] T.L┬¿u, J.Huang, High accuracy Nystr┬¿om approximations and their extrapolation for solving boundary weakly integral equations of the second kind, J. of Chinese Comp. Phy., 3(1997), 349-355.

[18] C.B.Lin, T.L┬¿u, T.M.Shih, The splitting extrapolation method, World Scientific, Singapore (1995).

[19] A.Sidi, M.Israrli, Quadrature methods for periodic singular Fredholm integral equations, J. Sci. Comput. , 3(1988),201-231.

[20] J.Huang, Z.Wang, Extrapolation algorithm for solving mixed boundary integral equations of the Helmholtz equation by mechanical quadrature methods. SIAM J. Sci. Comput. , Vol. 31, 6(2009), 4115-4129.

[21] P.M.Anselone, Collectively compact operator approximation theory, Prentice-Hall, Englewood Cliffs, New Jersey, 1971.