Numerical solution of a first kind integral equation of potential theory

References

• Atkinson , K. 1985a . Piecewise polynomial collocation for integral equations on surfaces in three dimensions . J. Integral Equations , 9 ( supplementary issue ) : 25 – 48 .
   Google Scholar
• Atkinson , K. 1985b . “ Solving integral equations on surfaces in space ” . In Constructive Methods for the Practical Treatment of Integral Equations , Edited by: Hämmerlin , G. and Hoffman , K. 20 – 43 . Basel : Birkhäuser .
   Google Scholar
• Atkinson , K. 1991 . Two-Grid Methods for Linear Integral Equations of the Second Kind on Piecewise Smooth Surfaces R .
   Google Scholar
• Atkinson , K. 1997 . The Numerical Solution of Integral Equations of the Second Kind , Cambridge University Press .
   Google Scholar
• Atkinson , K. 1993 . “ User's guide to a boundary element package for solving integral equations on piecewise smooth surface ” . In Reports on Computational Mathematics , Vol. 43 , Iowa City, Iowa : Department of Mathematics, University of Iowa .
   Google Scholar
• Chien , D. 1991 . “ Piecewise Polynomial Collocation for Integral Equations on Surfaces in Three Dimensions ” . In Ph. D. Thesis , Iowa City, Iowa : University of Iowa .
   Google Scholar
• Chen , Y. 1994 . “ Galerkin Methods for Solving Single Layer Integral Equations in Three Dimensions ” . In Ph. D. Thesis , Iowa City, Iowa : Univ. of Iowa .
   Google Scholar
• Flores , J. 1993 . The Conjugate Gradient Methods for Solving Fredholm Integral Equations of the Second Kind . Intern. J. Computer Math. , 48 : 77 – 94 .
   Web of Science ®Google Scholar
• Freund , R. , Golub , G. and Nachtigal , N. 1991 . Iterative solution of linear systems . Acta Numerica , 1 : 57 – 100 .
   Google Scholar
• Hestenes , M. and Stiefel , E. 1952 . Methods of conjugate gradients for solving linear systems . J. Res. Nat. Bur. Stand. , 49 : 409 – 439 .
   Google Scholar
• Huckbush , W. 1995 . Integral Equations; Theory and Numerical Treatment , Basel : Birkhäuser .
   Google Scholar
• Nabors , K. , Korsmeyer , F. , Leighton , F. and White , J. 1994 . Preconditioned, adaptive, multipole-accelerated iterative methods for three-dimensions first-kind integral equations of potential theory . SIAM J. Sci. Comp. , 15 : 713 – 735 .
   Web of Science ®Google Scholar
• Nachtigal , N. , Reddy , S. and Trefethen , L. 1992 . How fast are nonsymmetric matrix iterations? . SIAM J. Matrix Anal. Appl. , 13 : 778 – 795 .
   Web of Science ®Google Scholar
• Nedelec , J. 1976 . Curved finite element methods for the solution of singular integral equations on surfaces in R3 . Computer Methods in Appl. Mechanics and Engin. , 8 : 61 – 80 .
   Google Scholar
• von Petersdorff , T. and Stephan , E. 1992 . Multigrid solvers and preconditioners for first kind integral equations . Numerical Methods for Partial Diff. Eqns. , 8 : 443 – 450 .
   Google Scholar
• Saad , Y. and Shultz , M. 1986 . GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems . SIAM J. Sci. Stat. Comput. , 7 : 856 – 869 .
   Web of Science ®Google Scholar
• Sonneveld , P. 1989 . CGS, A fast Lanczos-type solver for nonsymmetric linear systems . SIAM J. Sci. Stat. Comput. , 10 : 36 – 52 .
   Web of Science ®Google Scholar
• Van der Vorst , H. 1992 . BI-CGSTAB: A fast and smoothly converging variant of BI-CG for the solution of nonsymmetric linear systems . SIAM J. Sci. Stat. Comput. , 13 : 631 – 644 .
   Web of Science ®Google Scholar
• Vavasis , S. 1992 . Preconditioning for boundary integral equations . SIAM J. Matrix Analysis , 13 : 905 – 925 .
   Web of Science ®Google Scholar