A Broadband Discrete Exterior Calculus A-Φ Formulation Solver with Sparsified Nested Dissection Ordering Preconditioner

A modified version of the sparsified nested dissection ordering technique is proposed as a broadband preconditioner for general comlex-valued, non-Hermitian indefinite matrix systems generated by the discrete exterior calculus
$\mathbf{A}-\Phi$
solver. Numerical examples indicate that the proposed preconditoner works for arbitrary frequencies with
$O(N\log N)$
complexity and the iterative solver takes almost a constant number of steps to converge regardless of
$N$
and the condition number. The proposed preconditioner is ideal for broadband and multi-scale analysis.