A relaxation method of an alternating iterative algorithm for the Cauchy problem in linear isotropic elasticity

作者：Marin Liviu^*; Johansson B Tomas

来源：Computer Methods in Applied Mechanics and Engineering, 2010, 199(49-52): 3179-3196.

DOI：10.1016/j.cma.2010.06.024

• Linear elasticity
• Inverse problem
• Cauchy problem
• Alternating iterative algorithm
• Relaxation procedures
• Boundary element method (BEM)

We propose two algorithms involving the relaxation of either the given Dirichlet data (boundary displacements) or the prescribed Neumann data (boundary tractions) on the over-specified boundary in the case of the alternating iterative algorithm of Kozlov et al. [16] applied to Cauchy problems in linear elasticity. A convergence proof of these relaxation methods is given, along with a stopping criterion. The numerical results obtained using these procedures, in conjunction with the boundary element method (BEM), show the numerical stability, convergence, consistency and computational efficiency of the proposed method.

• 出版日期2010