Efficient analysis of scattering by multiple moving objects using a tailored MLFMA

In this communication, we present a tailored multilevel fast multipole algorithm (MLFMA) for efficient analysis of scattering by multiple moving objects. There are two major issues with the conventional MLFMA for multiple moving targets. One is that the relative positions and attitudes of the targets change with time and we have to remesh the solution domain and refill the matrix elements at each simulation moment. The other is that we have to solve the matrix equations repeatedly for the moving targets. To alleviate these two burdens, we adopt the stationary grouping scheme in using the MLFMA for individual object, which is unchanged as the object is moving. With the grouping scheme, the near interactions are invariant, and most far interactions are reusable when the objects are in motions. The number of levels of MLFMA remains the same even if the overall dimension of the multiple targets is changing. The interactions between objects are expressed via coordinate transforms at the highest levels of their octrees. To accelerate the iterative solutions, the sparse approximate inverse preconditioner is incorporated. Numerical results show that the saving of CPU time is substantial for continuous simulations of a maneuvering process of a group of targets.