All‐at‐once solution of linear wave equations

Efficient parallel‐in‐time methods for hyperbolic partial differential equation problems remain scarce. Here we investigate an approach based on circulant preconditioned generalised minimal residual (GMRES) for the monolithic block Toeplitz equations which arise from constant time‐step discretizations. We present theoretical results which guarantee convergence in a number of iterations independent of the number of time‐steps and demonstrate the potential utility of the approach with numerical results employing several different finite difference schemes of varying orders of accuracy.