On an iterative solution of strongly nonsymmetric systems of linear algebraic equations

For an iterative solution of strongly nonsymmetric systems of linear algebraic equations we propose using a preconditioner that has the ILU structure but uses only the skew-symmetric part of the original matrix. We give sufficient conditions for the convergence of the Richardson method with this preconditioner, find optimal values of the iterative parameter, and give the results of numerical tests based on the solution of the stationary convection-diffusion equation with Péclet number from $10^3$ to $10^5$. We show that using such a preconditioner is effective in the solution of this class of problems by the GMRES method.