Parallelization in time through tensor-product space-time solvers

In this Note, we extend the fast tensor-product algorithm for the simulation of time-dependent partial differential equations. We use the natural tensorization of the space-time domain to propose, after discretization, a set of independent problems, each one with the complexity of a single steady problem. This allows for an efficient parallel implementation that is already interesting on small architectures, but that can also be combined with standard domain-decomposition-based algorithms providing a further direction of parallelism on large computer platforms. Preliminary numerical simulations are presented for a one-dimensional unsteady heat equation.