Null-Field Preconditioner With Selected Far-Field Contribution for 3-D Full-Wave EFIE

In this paper, a stable and effective preconditioner for the method of moments-based electric field integral equation matrix, based on the null-field method, is presented to expedite the convergence of Krylov subspace-based fast iterative solution. The preconditioner is computed from all near-field blocks and selected far-field blocks in accordance with the null-field procedure. The final form of the preconditioner is block diagonal, and therefore generates no additional fill-ins in its inverse and is also amenable to parallelization. A complexity analysis is presented to show the near-linear cost of preconditioner construction and usage in terms of computation time and memory. The numerical experiments with a sequential implementation demonstrate on an average 1.5-3× speed-up in the iterative solution time over threshold-dependent incomplete LU-based preconditioners.