Efficient shape parametrisation for automatic design optimisation using a partial differential equation formulation

This paper presents a methodology for efficient shape parametrisation for automatic design optimisation using a partial differential equation (PDE) formulation. It is shown how the choice of an elliptic PDE enables one to define and parametrise geometries corresponding to complex shapes. By using the PDE formulation it is shown how the shape definition and parametrisation can be based on a boundary value approach by which complex shapes can be created and parametrised based on the shape information at the boundaries or the character lines defining the shape. Furthermore, this approach to shape definition allows complex shapes to be parametrised intuitively using a very small set of design parameters. Thus, it is shown that the PDE based approach to shape parametrisation when combined with a standard method for numerical optimisation is capable of setting up automatic design optimisation problems allowing practical design optimisation to be more feasible.