Kronecker product splitting preconditioners for implicit Runge-Kutta discretizations of viscous wave equations

• Solution algorithms for implicit Runge–Kutta discretizations of viscous wave equations were studied.
• Preconditioning strategies based on the Kronecker product splitting were proposed.
• The method was found to be efficient and superior.

In this paper we study efficient iterative methods for solving the system of linear equations arising from fully implicit Runge-Kutta time discretization of a class of viscous wave equations. In each step of the time integration, a structured system of linear equations is obtained and needs to be solved numerically. A preconditioning strategy based on theKronecker product splitting of the coefficient matrix is applied to solve such linear systems. Some spectral properties of the preconditioned matrix are established and numerical examples are presented to demonstrate the effectiveness of this approach.