Condition number of the BEM matrix arising from the Stokes equations in 2D

Engineering Analysis with Boundary Elements

Volumn 32, Issue 9, 2008, Pages 736-746

  Dijkstra, W ^a   Mattheij, R M M ^a  

^a EINDHOVEN UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

Boundary element method; Condition number; Critical contour; Stokes equations

Indexed keywords

BOUNDARY CONDITIONS; BOUNDARY INTEGRAL EQUATIONS; FISH; INTEGRAL EQUATIONS; MATRIX ALGEBRA; NUMBER THEORY; NUMERICAL ANALYSIS; THEOREM PROVING;

(I ,J) CONDITIONS; BOUNDARY CONTOURS; BOUNDARY ELEMENTS; BOUNDARY INTEGRALS; CONDITION NUMBER (CN); DIRICHLET CONDITIONS; DISCRETE EQUATIONS; ELSEVIER (CO); NUMERICAL EXAMPLES; STOKES EQUATIONS; SYSTEM MATRICES;

BOUNDARY ELEMENT METHOD;

EID: 47049123873     PISSN: 09557997     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.enganabound.2007.10.005     Document Type: Article

References (24)

1. Christiansen S. Condition number of matrices derived from two classes of integral equations. Mat Meth Appl Sci 3 (1981) 364-392
2. Christiansen S. On two methods for elimination of non-unique solutions of an integral equation with logarithmic kernel. Appl Anal 13 (1982) 1-18
3. Christiansen S., and Hansen P.C. The effective condition number applied to error analysis of certain boundary colocation methods. J Comput Appl Math 54 (1994) 15-35
4. Christiansen S., and Saranen J. The conditioning of some numerical methods for the first kind boundary integral equations. J Comput Appl Math 67 (1996) 43-58
5. Dijkstra W., and Mattheij R.M.M. The condition number of the BEM-matrix arising from Laplace's equation. Electron J Boundary Elem 4 2 (2006) 67-81
6. Dijkstra W., and Mattheij R.M.M. A relation between the logarithmic capacity and the condition number of the BEM-matrices. Commun Numer Methods Eng 23 7 (2007) 665-680
7. Amini S., and Kirkup S.M. Solution of Helmholtz equation in the exterior domain by elementary boundary integral methods. J Comput Phys 118 (1995) 208-221
8. Kirkup S.M. The influence of the weighting parameter on the improved boundary element solution of the exterior Helmholtz equation. Wave Motion 93 (1992) 93-101
9. Kress R., and Spassov W.T. On the condition number of boundary integral operators for the exterior Dirichlet problem for the Helmholtz equation. Numer Math 42 (1983) 77-85
10. Hsiao G.C. On the stability of integral equations of the first kind with logarithmic kernels. Arch Ration Mech Anal 94 (1986) 179-192
11. Jaswon M.A., and Symm G. Integral equation methods in potential theory and elastostatics (1977), Academic Press, London
12. Power H., and Wrobel L.C. Boundary integral methods in fluid mechanics (1995), Computational Mechanics Publications, Southamption
13. Sloan I.H., and Spence A. The Galerkin method for integral equations of the first kind with logarithmic kernel: theory. IMA J Numer Anal 8 (1988) 105-122
14. Christiansen S., and Hougaard P. An investigation of a pair of integral equations for the biharmonic problem. J Inst Math Appl 22 (1978) 15-27
15. Costabel M., and Dauge M. On invertibility of the biharmonic single-layer potential operator. Integr Equations Oper Theory 24 (1996) 46-67
16. Fuglede B. On a direct method of integral equations for solving the biharmonic Dirichlet problem. Z Angew Math Mech 61 (1981) 449-459
17. Ladyzhenskaya O.A. The mathematical theory of viscous incompressible flow (1963), Gordon and Beach, New York, London
18. Pozrikidis C. Boundary integral and singularity methods for linearized viscous flows (1992), Cambridge University Press, Cambridge
19. Domínguez V., and Sayas F.J. A BEM-FEM overlapping algorithm for the Stokes equation. Appl Math Comput 182 (2006) 691-710
20. Vodicka R., and Mantic V. On invertibility of elastic single-layer potential operator. J Elasticity 74 (2004) 147-173
21. Costabel M. Boundary integral operators on Lipschitz domains: elementary results. SIAM J Math Anal 19 3 (1988) 613-626
22. McLean W. Strongly elliptic systems and boundary integral equations (2000), Cambridge University Press, Cambridge
23. Primo A.R.M., Wrobel L.C., and Power H. An indirect boundary-element method for slow viscous flow in a bounded region containing air bubbles. J Eng Math 37 (2000) 305-326
24. van der Vorst G.A.L., Mattheij R.M.M., and Kuiken H.K. Boundary element solution for two-dimensional viscous sintering. J Comput Phys 100 (1992) 50-63