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) the monolithic block Toeplitz equations which arise from constant time-step discretizations. We present theoretical results guarantee convergence in a number of iterations independent time-steps and demonstrate potential utility with numerical employing several different finite difference schemes varying orders accuracy.