The block gauss-seidel method in sound transmission problems

Abstract

Sound transmission through partitions can be modelled as an acoustic fluid-elastic structure interaction problem. The block Gauss-Seidel iterative method is used in order to solve the finite element linear system of equations. The blocks are defined in a natural way, respecting the fluid and structural domains. The convergence criterion (spectral radius of iteration matrix smaller than one) is analysed and interpreted in physical terms by means of simple one-dimensional problems. This analysis highlights the negative influence on the convergence of a strong degree of coupling between the acoustic domains. A selective coupling strategy has been developed and successfully applied to problems with strong coupling (i.e. sound transmission through double walls).