Block preconditioning strategies for nonlinear viscous wave equations

In this paper, five block preconditioning strategies are proposed to solve a class of nonlinear viscous wave equations. Implicit time-integration techniques from low order to high order are considered exclusively including implicit Euler (IE1) method, backward differentiation formulas (BDF2, BDF3) as well as the Crank–Nicholson (CN2) scheme. The CN2 method demonstrates superior performance compared to the BDF2 scheme for the problems considered in this work. In addition, the third-order accurate BDF3 scheme is found to be the most efficient in terms of computational cost for a prescribed accuracy level. Moreover, the benefit of this scheme increases for tighter error tolerances.