Conjugate Gradient–Boundary Element Method for the Cauchy Problem in Elasticity

In this paper, an iterative algorithm based on the conjugate gradient method (CGM) in combination with the boundary element method (BEM) for obtaining stable approximate solutions to the Cauchy problem in linear elasticity is analysed. An efficient stopping criterion for the CGM proposed by Nemirovskii in 1986 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.