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A preconditioning strategy for boundary element Galerkin methods

✍ Scribed by W. McLean; T. Tran

Publisher
John Wiley and Sons
Year
1997
Tongue
English
Weight
165 KB
Volume
13
Category
Article
ISSN
0749-159X

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✦ Synopsis

The Dirichlet and Neumann problems for the Laplacian are reformulated in the usual way as boundary integral equations of the first kind with symmetric kernels. These integral equations are solved using Galerkin's method with piecewise-constant and piecewise-linear boundary elements, respectively. In both cases, the stiffness matrix is symmetric and positive-definite, and has a condition number of order N , the number of degrees of freedom. By contrast, the condition number of the product of the two stiffness matrices is bounded independently of N . Hence, we can use the Neumann stiffness matrix to precondition the Dirichlet stiffness matrix, and vice versa.

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