Efficient Parallel-in-Time Preconditioned MINRES Solver for Wave Equations

The authors propose an absolute value block α-circulant preconditioner for the minimal residual (MINRES) method to solve the all-at-once linear system arising from the discretization of wave equations. The proposed preconditioner is Hermitian positive definite, enabling its use with the MINRES solver, and achieves a matrix-size independent convergence rate.