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Diagonal scaling of stiffness matrices in the Galerkin boundary element method

Published online by Cambridge University Press:  17 February 2009

Mark Ainsworth ,
Bill McLean  and
Thanh Tran
Mark Ainsworth
Affiliation:
Mathematics Department, Strathclyde University, 26 Richmond St, Glasgow G1 1XH, Scotland.
Bill McLean
Affiliation:
School of Mathematics, The University of New South Wales, Sydney 2052, Australia.
Thanh Tran
Affiliation:
Centre of Mathematics and its Applications, School of Mathematical Sciences, Australian National University, Canberra 0200, Australia.
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Abstract

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A boundary integral equation of the first kind is discretised using Galerkin's method with piecewise-constant trial functions. We show how the condition number of the stiffness matrix depends on the number of degrees of freedom and on the global mesh ratio. We also show that diagonal scaling eliminates the latter dependence. Numerical experiments confirm the theory, and demonstrate that in practical computations involving strong local mesh refinement, diagonal scaling dramatically improves the conditioning of the Galerkin equations.

Type
Research Article
Information
The ANZIAM Journal , Volume 42 , Issue 1 , July 2000 , pp. 141 - 150
Copyright
Copyright © Australian Mathematical Society 2000

References

[1]Ainsworth, M., McLean, W. and Tran, T., “The conditioning of boundary element equations on locally refined meshes and preconditioning by diagonal scaling”, SIAM J. Numer. Anal. 36 (1999) 1901–1932.Google Scholar
[2]Bank, R. E. and Scott, L. R., “On the conditioning of finite element equations with highly refined meshes”, SIAM J. Numer. Anal. 26 (1989) 1383–1394.Google Scholar
[3]Carstensen, C. and Stephan, E. P., “A posteriori error estimates for boundary element methods”, Math. Comp. 64 (1995) 483–500.Google Scholar
[4]Forsythe, G. E. and Moler, C. B., Computer Solution of Linear Algebraic Systems (Prentice-Hall, 1967).Google Scholar
[5]McLean, W. and Tran, T., “A preconditioning strategy for boundary element Galerkin methods”, Numer. Methods Partial Differential Eq. 13 (1997) 283–301.3.0.CO;2-J>CrossRefGoogle Scholar