A stable fast solver for quasi-Helmholtz decomposition methods

This work presents a fast solver that always annihilates the divergence of solenoidal functions, independent of the precision of the compressed impedance matrix elements. The solver is obtained by compressing a loop-tree transformed impedance matrix by using a properly tailored fast solver. Then the impedance matrix in the usual (and undecomposed) RWG basis is reconstructed by a linear-in-complexity inversion of the entire loop-tree transformation matrix and of its transpose. The resulting solver will prove to be extremely effective in keeping the EFIE condition number independent from the fast solver compression rate. Numerical results will show the effectiveness of the proposed method.