PRECONDITIONED KRYLOV SUBSPACE METHODS FOR BOUNDARY ELEMENT SOLUTION OF THE HELMHOLTZ EQUATION

[1]  H. R. Kutt The numerical evaluation of principal value integrals by finite-part integration , 1975 .

[2]  R. Kress,et al.  Integral equation methods in scattering theory , 1983 .

[3]  An iterative solution strategy for boundary element equations from mixed boundary value problems , 1994 .

[4]  Martin H. Gutknecht,et al.  Variants of BICGSTAB for Matrices with Complex Spectrum , 1993, SIAM J. Sci. Comput..

[5]  S. M. Kirkup,et al.  Solution of Helmholtz Equation in the Exterior Domain by Elementary Boundary Integral Methods , 1995 .

[6]  Francis X. Canning Sparse Approximation for Solving Integral Equations with Oscillatory Kernels , 1992, SIAM J. Sci. Comput..

[7]  M. Hestenes,et al.  Methods of conjugate gradients for solving linear systems , 1952 .

[8]  Kendall E. Atkinson,et al.  Iterative Solution of Linear Systems Arising from the Boundary Integral Method , 1992, SIAM J. Sci. Comput..

[9]  Economical solution technique for boundary integral matrices , 1983 .

[10]  C. Lanczos Solution of Systems of Linear Equations by Minimized Iterations1 , 1952 .

[11]  Lloyd N. Trefethen,et al.  How Fast are Nonsymmetric Matrix Iterations? , 1992, SIAM J. Matrix Anal. Appl..

[12]  W. Wendland,et al.  The fourier series representation of pseudo-differentiai operators on closed curves , 1987 .

[13]  David E. Keyes,et al.  Preconditioned Krylov solvers for BEA , 1994 .

[14]  K. Atkinson,et al.  A survey of numerical methods for the solution of Fredholm integral equations of the second kind , 1977 .

[15]  D. Arnold,et al.  The convergence of spline collocation for strongly elliptic equations on curves , 1985 .

[16]  G. F. Miller,et al.  The application of integral equation methods to the numerical solution of some exterior boundary-value problems , 1971, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[17]  Frank J. Rizzo,et al.  On boundary integral equations for crack problems , 1989, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[18]  Henk A. van der Vorst,et al.  Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems , 1992, SIAM J. Sci. Comput..

[19]  Chen Ke,et al.  Conjugate gradient method for second kind integral equations — applications to the exterior acoustic problem , 1989 .

[20]  Mauricio Pazini Brandao,et al.  Improper integrals in theoretical aerodynamics - The problem revisited , 1987 .

[21]  Y. Saad,et al.  GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems , 1986 .

[22]  S. Amini Boundary integral solution of the exterior Helmholtz problem , 1993, Computational Mechanics.

[23]  P. Sonneveld CGS, A Fast Lanczos-Type Solver for Nonsymmetric Linear systems , 1989 .

[24]  Ian H. Sloan,et al.  On the numerical solution of a logarithmic integral equation of the first kind for the Helmholtz equation , 1993 .

[25]  J.C.F. Telles,et al.  Iterative solution of bem equations by GMRES algorithm , 1992 .

[26]  I. S. Gradshteyn,et al.  Table of Integrals, Series, and Products , 1976 .

[27]  Yi Yan The collocation method for first-kind boundary integral equations on polygonal regions , 1990 .

[28]  R. Kress Minimizing the condition number of boundary integral operators in acoustic and electromagnetic scattering , 1985 .

[29]  R. Coifman,et al.  Fast wavelet transforms and numerical algorithms I , 1991 .

[30]  S. Amini On the choice of the coupling parameter in boundary integral formulations of the exterior acoustic problem , 1990 .

[31]  V. Rokhlin Rapid solution of integral equations of classical potential theory , 1985 .

[32]  Stephen A. Vavasis,et al.  Preconditioning for Boundary Integral Equations , 1992, SIAM J. Matrix Anal. Appl..

[33]  Wolfgang Dahmen,et al.  Wavelet approximation methods for pseudodifferential equations II: Matrix compression and fast solution , 1993, Adv. Comput. Math..