An Adjoint Based Implementation of the Parareal Algorithm

AbstractThis paper presents a new ‘Parareal-algorithm’ to solve time-dependent ODEs parallel in time. The algorithm approximates the solutions later in time simultaneously with the solutions earlier in time. To approximate the solutions simultaneously, an optimization problem is constructed and solved using gradient based techniques. The accurate gradients are evaluated using adjoints. Promising results are obtained when the interval of interest is split into suffciently small subintervals