Time Parallelization for Nonlinear Problems Based on Diagonalization

The direct time parallelization method based on diagonalization is only applicable to linear problems. We propose here a new method based on diagonalization which permits the direct parallelization in time of a Newton iteration that works simultaneously over several time steps. We first explain the method for a scalar model problem, and then give a formulation for a nonlinear partial differential equation based on tensorization. We illustrate the methods with numerical experiments.