Parallel in time methods partition the time domain such that adjacent time slices can be parallelised and run simultaneously. Iteratively, the input to each time slice is supplied by the output from an adjacent time slice. In this way, it is possible to iteratively simulate an unsteady/cyclic variation wherein early iterations provide a low fidelity prediction of the (high fidelity) final solution.

Most engineering design problems comprise different disciplines, and have a number of performance measures. It is also common for computational simulation times to be relatively expensive. Thus, there is an important need to facilitate multi-objective, multi-disciplinary design optimisation leading to design improvement. Kriging based surrogate modeles of multiple objectives can be exploited in non-sorting genetic algorithm methods (e.g. NSGA-II) to seek optimal design solutions in a realistic time-frame.

Following an idea proposed by Rob Lewis (now at TotalSim) it is possible to drive a design process using an inner loop of cheap simulations in which parameterised flow features are captured using an inverse design method, such that an expensive objective function is optimised in an outer loop.

Many design problems present significant challenges with respect to the number of design parameters and to the locations of local and global optimal configurations. It is possible to address these challenges by parameter space reduction methods (e.g. proper orthogonal decomposition) and/or by two or more stages of exploration/exploitation (e.g 2D into 3D simulations).

One of our earliest forrays into optimisation involving expensive computational simulations was based on the recognition that surrogate modelling strategies can effectively employ partially converged data in the selection of update points.