The numerical solution of the Helmholtz model with complex coefficients is considered. This PDE problem is split into real and imaginary parts and so transformed into a coupled system of two Helmholtz problems with real coefficients. Associated iterative models at both continuous and discrete levels are proposed. The convergence of these, Block SOR type, iterative methods for solving the linear algebraic system of equations associated with the 5-point-star Helmholtz discretization is analyzed. Numerical experiments which confirm the theoretical results and exhibit the effectiveness of the proposed schemes are presented.

basic iterative methods, Helmholtz equation, finite difference, underwater acoustics.