Multilevel Adaptive Cross Approximation (MLACA)

The Multilevel Adaptive Cross Approximation (MLACA) is proposed as a fast method to accelerate the matrix-vector products in the iterative solution of the linear system that results from the discretization of electromagnetic Integral Equations (IE) with the Method of Moments (MoM). The single level ACA, already described in the literature, is extended with a multilevel recursive algorithm in order to improve the asymptotical complexity of both the computational cost and the memory requirements. The main qualities of ACA are maintained: it is purely algebraic and independent of the integral equation kernel Green´s function as long as it produces pseudo-rank-deficient matrix blocks. The algorithm is presented in such a way that it can be easily implemented on top of an existing MoM code with most commonly used Green´s functions.