Performance of Preconditioned Krylov Iterative Methods for Solving Hybrid Integral Equations in Electromagnetics

In solving systems of linear equations arising from practical engineering models such as the electromagnetic wave scattering problems, it is critical to choose a fast and robust solver. Due to the large scale of those problems, preconditioned Krylov iterative methods are most suitable. The Krylov iterative methods require the computation of matrix-vector product operations at each iteration, which account for the major computational cost of this class of methods. We use the multilevel fast multipole algorithm (MLPMA) to reduce the computational complexity of the matrix-vector product operations. We conduct an experimental study on the behavior of three Krylov iterative methods, BiCG, BiCGSTAB, and TFQMR, and of two preconditioners, the ILUT preconditioner, and the sparse approximate inverse (SAI) preconditioner. The preconditioners are constructed by using the near part matrix numerically generated in the MLFMA. Our experimental results indicate that a well chosen preconditioned Krylov iterative method maintains the computational complexity of the MLFMA and effectively reduces the overall simulation time.