An Inverse-Based Multifrontal Block Incomplete LU Preconditioner for the 3-D Finite-Element Eigenvalue Analysis of Lossy Slow-Wave Structures

In this paper, a novel inverse-based multifrontal block incomplete LU preconditioner is proposed, which is derived from the complete multifrontal method and the inverse-based dropping strategy. The new preconditioner is used to solve the large-scale complex unsymmetrical linear systems arising from the 3-D finite-element (FE) eigenvalue analysis of lossy slow-wave structures (SWSs) of traveling-wave tubes (TWTs). An update-matrix-free multifrontal method and an adaptive super-block incomplete factorization framework are proposed and utilized to improve the computational performance and decrease the memory requirements of this preconditioner. Moreover, the inverse-based dropping strategy is introduced to the incomplete multifrontal method for the first time making this preconditioner more effective. By utilizing the proposed preconditioner, the cold characteristic parameters of SWSs can be calculated quickly and accurately. In the simulations of many SWSs, the 3-D FE eigenvalue analysis of lossy SWSs based on this preconditioner has shown the high-efficiency computational performance and the low memory requirements. It is shown that this novel preconditioner is very useful to design lossy SWSs for high-efficiency TWTs.