Block Krylov Recycling Algorithms for FETI-2LM Applied to 3-D Electromagnetic Wave Scattering and Radiation

Abstract

To solve multisource electromagnetic problems, a new way of using Krylov type iterative algorithms is presented to improve the finite-element tearing and interconnecting domain decomposition method with two Lagrange multipliers (FETI-2LMs). There are three main ingredients in the proposed algorithms: 1) a recycling Krylov method is used to solve the condensed interface problem introduced by the FETI-2LM method; 2) all the search direction vectors for all the successive sources are stored and used to build a projection, which decreases the number of iterations for the successive sequences of ORTHODIR Krylov iterations; and 3) successive problems are solved with a block technique preserving the numerical efficiency of the previous recycling Krylov strategy and greatly improving the parallel efficiency of the method. Performances and accuracy of the proposed block Krylov recycling strategy will be discussed based on the simulation of two engineering applications (monostatic radar cross section of large antenna array and radiating element coupling of an antenna array) and the comparison of the simulated results with measurements. For the most difficult configuration of linearly independent right hand-sides (TEM mode ports), a speedup of 11.7 is observed, while for linearly dependent right hand-sides (plane wave excitations), the speedup of 115 obtained by the proposed method outperforms those obtained with the existing recycling Krylov techniques already published and applied to FETI solved electromagnetic problems (speedup of 1.7).