Sparse approximate inverse preconditioner for multiscale dynamic electromagnetic problems

Abstract

Citation:Pan, X.-M., and X.-Q. Sheng (2014) Abstract The inherent difficulties of traditional preconditioning techniques are revealed by numerically analyzing characteristics of method of moments systems with respect to multiscale dynamic electromagnetic applications. Techniques are developed to solve these difficulties for the traditional sparse approximate inverse preconditioner. The proposed techniques include a skeleton-based filtering strategy aiming to overcome the awkward filtering strategy extensively employed in traditional preconditioners and the strategy to recover the block structure of the inverse matrix. The proposed techniques are investigated by numerical experiments on complex targets.

Preconditioning for Large-Scale Boundary Integral Equations in Electromagnetics [Open Problems in CEM]

“…Owing to its inherent parallelism and attractive numerical stability, the SPAI preconditioner has become a popular choice in the electromagnetic community, being used for solving extremely large dense matrix problems [13,18,19]. …”

“…Another strategy positively investigated to relax the limita tions due to the lack of global couplings is to utilize the inter polative decomposition "skeletonization," which is equivalent to ranking and ordering principal basis/testing functions according to their capability of radiation/receiving [19].…”

On a refinement-free Calderón multiplicative preconditioner for the electric field integral equation

“…Different strategies have been presented to overcome the dense-discretization breakdown. A first class of techniques relies on algebraic strategies such as the incomplete LU factorization [12,13], sparse approximate inverse [14,15], or near-range preconditioners [16]. While they improve the conditioning, the condition number still grows with decreasing h.…”

Well-conditioned algorithm for scattering by a few eccentrically multilayered dielectric circular cylinders

“…Thus, alleviation of any difficulty along the implementation of an analytical model in a numerically stable fashion has utmost importance. The relevant concerns in the past five decades are issued in the context of implementation of the analytical formulations efficiently in computer [Bates, 1975;Ivanov, 1968;Poyedinchuk et al, 2000;Yiğit and Dikmen, 2011;Bruno and Lintner, 2012;Dikmen et al, 2013;Sever et al, 2014;Sandström and Akeab, 2014;Pan and Sheng, 2014].…”

“…Despite the excessive memory and processor resources of the modern computers, these criteria are circumstantial [Poyedinchuk et al, 2000] because the only practical way to obtain a reliable and stable solution avoiding the round-off errors is making sure that the condition number of the truncated algebraic system does not reach (preferably) or exceed (meaning, no significant digits are obtained) the power of the mantissa length (i.e., 2 53 ≈ 10 16 for standard PC) [Poyedinchuk et al, 2000;Wilkinson, 1975]. This problem was elaborated in Sever et al [2014] for a pair of impedance circular cylinders; in Poyedinchuk et al [2000], Sandström and Akeab [2014], and Pan and Sheng [2014] for a wider class of geometries; in [Yiğit and Dikmen [2011] and Bruno and Lintner [2012] for open 2-D geometries; and in Ivanov [1968] for pairs of canonic shapes. Basically, they aim at reducing the LAES1 into a linear algebraic equation system of the second kind (LAES2) in l 2 (i.e., the functional space of square summable sequences).…”