Radial basis function for parallel mesh-to-mesh interpolation in solving fluid-structure interaction problem

In strongly coupled fluid-structure interaction simulations, the fluid dynamics and solid dynamics problems are solved independently on their own meshes. Therefore, it becomes necessary to interpolate the physical properties (pressure, displacement) across two meshes. In the present paper, we propose to accelerate the interpolation process by the method of radial basis functions using the matrix-free solution of the system of equations on a GPU. Also, we reduce the number of equations in the system by using an adaptive algorithm for choosing interpolation points. The adaptive algorithm allows to reduce the number of equations of the interpolation system while preserving the quality of the interpolation. Estimation of the effectiveness of reducing the computational costs based on the matrix-free approach to solving the system, as well as evaluating the quality of interpolation, was carried out using the simulation of the problem of modeling the flow of fluid with a supersonic deformable nozzle.