Before revision: Solving wave equations in a time-parallel manner is challenging, and the algorithm based on the block \alpha-circulant preconditioning technique has shown its advantage in many existing studies (where \alpha\in(0, 1) is a free parameter).
After revision: Solving evolutionary equations in a time-parallel manner is challenging, and the algorithm based on the block \alpha-circulant preconditioning technique has shown its advantage in many existing studies (where \alpha\in(0, 1) is a free parameter).