ISSN:
0029-5981
Keywords:
boundary element method (BEM)
;
singular value decomposition (SVD)
;
L-curve method
;
Engineering
;
Numerical Methods and Modeling
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mathematics
,
Technology
Notes:
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 unspecified 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 unspecified higher-order boundary derivatives data. In order to overcome this difficulty, 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 Wiley & Sons, Ltd.
Additional Material:
7 Ill.
Type of Medium:
Electronic Resource
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