Towards surrogate models of large scale parametric industrial flow problems

Computer simulations are an increasingly important tool to support virtual prototyping in science and engineering as they enable to reduce the time and cost of experimental testing. Virtual design aims to identify the best configuration of a system by testing several values of parameters that characterise various aspects such as geometric features (e.g., the length of a beam) or material properties (e.g., the density of a fluid). These quantities are incorporated in the mathematical model of the system by parametrising the underlying equations. The resulting parametric problem is then solved numerically to identify the optimal configurations. However, this task is computationally very demanding. In fact, in practical 3D applications, numerical models can involve millions of unknowns and must be solved multiple times for each possible configuration of the system. Novel fast and reliable algorithms are thus needed to make the computational cost affordable. This is a very challenging research area of great practical importance for many applications such as optimal design of filtration systems and aerodynamic simulations in the automotive industry. This project will contribute to this field by developing a new computational framework that combines two mathematical methods: domain decomposition and proper generalised decomposition. These will be used to split parametric problems into collections of simpler subproblems, to solve them independently accounting for all significant values of the parameters, and to 'glue' the local solutions to obtain those of the original problems. The proposed project will contribute to advance the state-of-the-art in numerical mathematics and develop effective algorithms for scientists and engineers that use virtual design by computational modelling.