A new fast and rapidly converging method for the solution of the electric field integral equation

Abstract

This paper presents a new fast matrixvector multiplication scheme for the solution of the Electric Field Integral Equation.Similarly to other fast methods, our approach reduces the matrixvector multiplication cost from O(N 2 ) to O(N log N ). Differently from other fast solvers, however, the effectiveness of EFIE preconditioning techniques such as quasi-Helmholtz decompositions or Calderón approaches is maintained by our method even for very high matrix compression rates. This is thanks to the fact that, in the scheme we are proposing, the contribution from the scalar potential when applied to or tested with solenoidal functions is always zero independent of the compression error. In addition, the new method will take advantage of the redundancies of the EFIE matrix in the low-frequency/dense discretization regime, and it will further decrease both the memory storage and the multiplication cost with respect to currently available fast solvers. Numerical results will show the effectiveness of our approach and its impact on the solution of realistic problems.

Acceleration of the Calderón preconditioned PMCHWT solver by the asynchronously parallelized NSPWMLFMA

“…This jeopardized the workings of the Calderón preconditioner which hinges, as explained above, on the ability of the basis functions to form loops. An algorithm designed to avoid these problems can be found in [7]. This low frequency behavior and the techniques described in [7] were not investigated in this contribution and form the subject of future research.…”