Efficient solution to the large scattering and radiation problem using the improved finite-element fast multipole method

The finite-element hybridized with the boundary integral (BI) method is a powerful technique to solve the complex scattering and radiation problems (where the fast multipole method is often employed to accelerate the calculation of the BI). However, this hybrid method suffers from a very slow convergence rate because the finite-element matrix is an ill-conditioned one. In this paper, we use the multifrontal method to perform the triangular factorization of this ill-conditioned finite-element matrix. This improves the spectral property of the whole matrix and makes the hybrid method converge very fast. Through some numerical examples, including the scattering from a real-life aircraft model, the accuracy and efficiency of this improved hybrid method are demonstrated.