Study on a Fast Solver for Combined Field Integral Equations of 3D Conducting Bodies Based on Graph Neural Networks

In this paper, we present a graph neural networks (GNNs)-based fast solver (GraphSolver) for solving combined field integral equations (CFIEs) of 3D conducting bodies. Rao-Wilton-Glisson (RWG) basis functions are employed to discretely and accurately represent the geometry of 3D conducting bodies. A concise and informative graph representation is then constructed by treating each RWG function as a node in the graph, enabling the flow of current between nodes. With the transformed graphs, GraphSolver is developed to directly predict real and imaginary parts of the x, y and z components of the surface current densities at each node (RWG function). Numerical results demonstrate the efficacy of GraphSolver in solving CFIEs for 3D conducting bodies with varying levels of geometric complexity, including basic 3D targets, missile-shaped targets, and airplane-shaped targets.