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Conjugate gradient-boundary element method for the Cauchy problem in elasticity . (English) Zbl 1038.74048

Summary: We analyze an iterative algorithm based on the conjugate gradient method (CGM) in combination with the boundary element method (BEM) for obtaining stable approximate solutions to Cauchy problem in linear elasticity. An efficient stopping criterion for the CGM proposed by A. S. Nemirovskij [U.S.S.R. Comput. Math. Math. Phys. 26, No. 2, 7–16 (1986); translation from Zh. Vychisl. Mat. Mat. Fiz. 26, No. 3, 332–347 (1986; Zbl 0615.65056)] is employed, and in addition the accuracy of the iterative algorithm is improved by using a variable relaxation procedure. The numerical results obtained confirm that the iterative BEM produces a convergent and stable numerical solution with respect to increasing the number of boundary elements and decreasing the amount of noise added into the input data.

MSC:

74S15 Boundary element methods applied to problems in solid mechanics
74B05 Classical linear elasticity

Citations:

Zbl 0615.65056
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