Fast solution of BEM systems for elasticity problems using wavelet transforms

References

• Amaratunga , K. 2000 . A wavelet based approach for compressing kernel data in large-scale simulations for 3D integral problems . Comput. Sci. Eng. , 1 : 34 – 45 .
   Google Scholar
• Banerjee , P. K. 1994 . The Boundary Element Method in Engineering , London : McGraw-Hill .
   Google Scholar
• Barra , L. P.S. 1994 . Iterative solution of BEM equations by GMRES . Comput. Struct. , 111 : 335 – 355 .
   Google Scholar
• Becker , A. A. 1991 . The Boundary Element Method in Engineering , London : McGraw-Hill .
   Google Scholar
• Beylkin , G. , Coifman , R. and Rokhlin , V. 1991 . Fast wavelet transforms and numerical algorithms I . Comm. Pure. Appl. Math. , 44 : 141 – 183 .
   Web of Science ®Google Scholar
• Bond , D. M. and Vavasis , S. A. 1994 . Fast wavelet transforms for matrices arising from boundary element methods , Cornell University . Computer Science Research Report, TR-174
   Google Scholar
• Bucher , H. F. and Wrobel , L. C. 2002 . A novel approach to applying fast wavelet transforms in the boundary element method . Electron. J. Bound. Elem. , 2 : 187 – 195 .
   Google Scholar
• Bucher , H. F. 2003 . Fast solution of problems with multiple load cases by using wavelet compressed boundary element matrices . Commun. Numer. Math. Eng. , 19 : 387 – 399 .
   Google Scholar
• Bucher , H. F. 2004 . On the block wavelet transform applied to the boundary element method . Eng. Anal. Bound. Elem. , 28 : 571 – 581 .
   Google Scholar
• Chen , K. 1999 . Discrete wavelet transforms accelerated sparse preconditioners for dense boundary element systems . Electron. Trans. Numer. Anal. , 8 : 138 – 153 .
   Google Scholar
• Dahmen , W. 1996 . “ Multiscale methods for the solution of the Helmholtz and Laplace equations ” . In Boundary Element Topics , Edited by: Wendland , Wlfgang L. Stuttgart : Springer-Verlag .
   Google Scholar
• Daubecies , I. 1992 . Ten Lectures on Wavelets , Vol. 61 , Philadelphia : SIAM .
   Google Scholar
• Gonzalez , P. , Cabalaeir , J. C. and Pena , T. F. 2002 . Parallel iterative solvers involving fast wavelet transforms for the solution of BEM systems . Adv. Eng. Software. , 33 : 417 – 426 .
   Google Scholar
• Greengard , L. and Rokhlin , V. 1987 . A fast algorithm for particle simulations . J. Comput. Phys. , 73 : 325 – 348 .
   Web of Science ®Google Scholar
• Hackbush , W. and Nowak , Z. P. 1989 . On the fast matrix multiplication in the boundary element method by panel clustering . Numer. Math. , 54 : 463 – 491 .
   Google Scholar
• Keinert , F. 2003 . Wavelets and Multiwavelets , Boca Raton, FL : Chapman and Hall CRC Press .
   Google Scholar
• Koro , K. and Abe , K. 2003 . A practical determination strategy of optimal threshold parameter for matrix compression in wavelet BEM . Int. J. Numer. Meth. Eng. , 57 : 169 – 191 .
   Google Scholar
• Lage , C. and Schwab , C. 1990 . Wavelet Galerkin algorithms for boundary integral equations . SIAM J. Sci. Comput. , 20 : 195 – 222 .
   Google Scholar
• Mansur , W. J. , Araujo , F. C. and Malgnini , JEB . 1992 . Solution of BEM systems of equations via iterative techniques . Int. J. Numer. Meth. Eng. , 33 : 1823 – 1841 .
   Google Scholar
• Ravnik , J. , Skerget , L. and Hibersek , M. 2004 . The wavelet transform for BEM computational fluid dynamics . Eng. Anal. Bound. Elem. , 28 : 1303 – 1314 .
   Google Scholar
• Rokhlin , V. 1983 . Rapid solution of integral equations of classical potential theory . J. Comput. Phys. , 60 : 187 – 207 .
   Google Scholar
• Saad , Y. and Schultz , M. H. 1986 . GMRES: a generalized minimal residual method for solving nonsymmetric linear systems . SIAM. J. Sci. Stat. Comput. , 7 : 856 – 869 .
   Web of Science ®Google Scholar
• Williams , J. R. and Amaratunga , K. 1994 . Introduction to the wavelets in the engineering . Int. J. Numer. Meth. Eng. , 37 : 2365 – 2388 .
   Web of Science ®Google Scholar