A high-order time-parallel scheme for solving wave propagation problems via the direct construction of an approximate time-evolution operator

The manuscript presents a new technique for computing the exponential of
skew-Hermitian operators. Principal advantages of the proposed method include:
stability even for large time-steps, the possibility to parallelize in time
over many characteristic wavelengths, and large speed-ups over existing methods
in situations where simulation over long times are required. Numerical examples
involving the 2D rotating shallow water equations and the 2D wave equation in
an inhomogenous medium are presented, and the method is compared to the 4th
order Runge-Kutta (RK4) method and to the use of Chebyshev polynomials. Is is
demonstrated that the new method achieves high accuracy over long time
intervals, and with speeds that are orders of magnitude faster than both RK4
and the use of Chebyshev polynomials.