Iterative solution of bem equations by GMRES algorithm

A fast BEM for the analysis of damaged structures with bonded piezoelectric sensors

“…In this context, the use of hierarchical matrices [29][30][31] for the representation of BEM systems of equations, in conjunction with Krylov subspace methods [32][33][34][35], constitutes a recent and interesting development. Such a technique allows to speed up the computation maintaining the required accuracy and saving the storage memory needed for the collocation matrix treatment.…”

An efficient implementation of the generalized minimum residual algorithm with a new preconditioner for the boundary element method

“…Nonetheless, it still suffers from slow convergence rates [2,11,12] and unexpected breakdown in a practical engineering problem of the BEM [13] because the coefficient matrix of the BEM is too ill-conditioned. Additionally, the restarted version of GMRES algorithm, which has been considered as the standard remedy to the unexpected breakdown and the large memory requirements, can still make the convergence rates worse [14] and fail to converge by the complete stagnation [15].…”

Performance of GMRES for the MFS

“…We shall experiment by taking the pre-conditioner P to be a diagonal matrix consisting of the diagonal elements of G d . Such pre-conditioners were found to be effective when using GMRES to solve systems resulting from Boundary Element Method (BEM) discretizations [7][8][9].…”