Improved buffered block forward backward method applied to 3D scattering problems

This paper presents an improved buffered block forward backward (BBFB) technique for the solution of 3D wave scattering problems. The BBFB method displays rapid convergence when the eigenvalues of the associated iteration matrix are small. Conversely when the eigenvalues are large it displays poorer convergence. The optimised step presented in this paper helps to circumvent the poor convergence of the forward backward method in the latter case by introducing an optimally sized correction in the approximate direction of the eigenvector associated with the iteration matrix's dominant eigenvalue. Numerical results are presented in order to demonstrate the convergence of the improved BBFB method.