Scalable high-order algorithms for wakefield simulations

We developed a high-order algorithm in time for our spectral-element discontinuous Galerkin time-domain electromagnetic code NekCEM. High-order spatial approximations are known to be the most efficient scheme guaranteeing a certain level of accuracy after long simulation time due to less numerical dispersion. We investigate an explicit type time stepping method, exponential timeintegration method, based on Krylov approximation which can possibly accel efficiency by allowing larger time step size with the total number of timestep reduction for accelerator applications. Computational results are compared to those by the fourth-order Runge-Kutta method that has been widely used for high-order spatial operator for the Maxwell's equations. We demonstrate the parallel performance of the high-order time-integration scheme up to 8,192 processors achieving efficiency of 72%.