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The boundary element solution of the Laplace and biharmonic equations subjected to noisy boundary data

✍ Scribed by D. Lesnic; L. Elliott; D. B. Ingham

Publisher
John Wiley and Sons
Year
1998
Tongue
English
Weight
136 KB
Volume
43
Category
Article
ISSN
0029-5981

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✦ Synopsis

This study investigates the numerical solution of the Laplace and biharmonic equations subjected to noisy boundary data. Since both equations are linear, they are numerically discretized using the Boundary Element Method (BEM), which does not use any solution domain discretization, to reduce the problem to solving a system of linear algebraic equations for the unspeciÿed boundary values. It is shown that when noisy, lower-order derivatives are prescribed on the boundary, then a direct approach, e.g. Gaussian elimination, for solving the resulting discretized system of linear equations produces an unstable, i.e. unbounded and highly oscillatory, numerical solution for the unspeciÿed higher-order boundary derivatives data. In order to overcome this di culty, and produce a stable solution of the resulting system of linear equations, the singular value decomposition approach (SVD), truncated at an optimal level given by the L-curve method, is employed. ? 1998 John

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