A Parallel Two-Level Spectral Preconditioner for Fast Monostatic Radar Cross-Section Calculation
Keywords:
MLFMM, MUMPS, preconditioning, scattering problems, spectralAbstract
Although the Multilevel Fast Multipole Method (MLFMM) and the parallel technology can accelerate the matrix-vector product operation, the iteration number does not reduce at all in the iterative solution. A new proposed two-level spectral preconditioning technique is developed for the generalized minimal residual iterative method, in which the MLFMM is used to accelerate the calculation. The Multifrontal Massively Parallel Solver (MUMPS) is used to damp the high frequencies of the error, and the low frequencies of the error are eliminated by a spectral preconditioner in a two-level manner. This technique is a combination of MUMPS and a low-rank updated spectral preconditioner, in which the restarted deflated Generalized Minimal Residual (GMRES) with the newly constructed spectral two-level preconditioner is considered as the iterative method for solving subsequent systems. Numerical experiments indicate that the proposed preconditioner is efficient for the MLFMM and can significantly reduce both the iteration number and computational time.
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