Anisotropic mesh refinement: The conditioning of Galerkin boundary element matrices and simple preconditioners

SIAM Journal on Numerical Analysis

Volumn 44, Issue 4, 2006, Pages 1487-1513

  Graham, Ivan G ^a   McLean, William ^b  

^a University of Bath   (United Kingdom)

^b UNIVERSITY OF NEW SOUTH WALES   (Australia)

Author keywords

Anisotropic refinement; Boundary integral equations; Condition number estimates; Diagonal scaling; Galerkin approximation; Spectral bounds; Symmetric elliptic problems

Indexed keywords

ANISOTROPY; APPROXIMATION THEORY; ASYMPTOTIC ANALYSIS; BOUNDARY ELEMENT METHOD; BOUNDARY INTEGRAL EQUATIONS; FINITE ELEMENT METHOD; STIFFNESS;

ANISOTROPIC REFINEMENT; CONDITION NUMBER ESTIMATES; DIAGONAL SCALING; GALERKIN APPROXIMATION; SYMMETRIC ELLIPTIC PROBLEMS;

GALERKIN METHODS;

EID: 34547943679     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/040621247     Document Type: Article

References (12)

1. M. AINSWORTH, W. MCLEAN, AND T. TRAN, The conditioning of boundary element equations on locally refined meshes and preconditioning by diagonal scaling, SIAM J. Numer. Anal., 36 (1999), pp. 1901-1932.
2. M. AINSWORTH, W. MCLEAN, AND T. TRAN, Diagonal scaling of stiffness matrices in the Galerkin boundary element method, ANZIAM J., 42 (2000), pp. 141-150.
3. R. E. BANK AND L. R. SCOTT, On the conditioning of finite element equations with highly refined meshes, SIAM J. Numer. Anal., 26 (1989), pp. 1383-1394.
4. M. DAUGE, Elliptic Boundary Value Problems on Corner Domains, Lecture Notes in Math. 1341, Springer-Verlag, Berlin, 1988.
5. J. ELSCHNER, The double layer potential operator over polyhedral domains. II. Spline Galerkin methods, Math. Methods Appl. Sci., 15 (1992), pp. 23-37.
6. I. G. GRAHAM, W. HACKBUSCH, AND S. A. SAUTER, Hybrid Galerkin boundary elements on degenerate meshes, in Mathematical Aspects of Boundary Element Methods, Chapman & Hall/CRC Res. Notes Math. 414, M. Bonnet, A.-M. Sandig, and W. L. Wendland, eds., Chapman & Hall/CRC, Boca Raton, FL, 2000, pp. 140-151.
7. I. G. GRAHAM, W. HACKBUSCH, AND S. A. SAUTER, Finite elements on degenerate meshes: Inverse-type inequalities and applications, IMA J. Numer. Anal., 25 (2005), pp. 379-407.
8. W. HACKBUSCH AND Z. NOWAK, On the fast matrix multiplication in the boundary element method by panel clustering, Numer. Math., 54 (1989), pp. 463-491.
9. W. MCLEAN, Strongly Elliptic Systems and Boundary Integral Equations, Cambridge University Press, Cambridge, UK, 2000.
10. J. C. NÉDÉLEC, Integral equations with non-integrable kernels, Integral Equations Operator Theory, 4 (1982), pp. 563-572.
11. T. VON PETERSDORFF, Randwertprobleme der Elastizitätstheorie für Polyeder - Singularitäten und Approximation mit Randelementmethoden, Dissertation, Technische Hochschule Darmstadt, Darmstadt, Germany, 1989.
12. V. ROKHLIN, Rapid solution of the integral equations of classical potential theory, J. Comput. Phys., 60 (1985), pp. 187-207.