The impedance matrix localization (IML) method for moment-method calculations

AN OVERVIEW OF THE EVOLUTION OF METHOD OF MOMENTS TECHNIQUES IN MODERN EM SIMULATORS (Invited Paper)

“…Other techniques that take advantage of the efficient evaluation of fast matrix-vector products are the Complex Multipole Beam Approach (CMBA) [20], that relies on using a series of beams represented as Gabor functions on the scatterer boundary in order to reduce the size of the matrix under consideration, the combination of the Complex Source Beam and the Moment Method [21], that performs fast matrix-vector products by taking advantage of the directional properties of the Complex Source Beams representing the radiation from the basis elements included in each group, the Impedance Matrix localization (IML) technique [22], which, in turn, aims to sparsify the impedance matrix by introducing special basis and test functions that localize the important interactions to only a small number of elements in the matrix, the Adaptive Integral Method (AIM) [23], which exploits the Toeplitz property of the Green's function kernel to reduce storage and accelerate the matrixvector products by making use of the Fast Fourier Transform, or the Multilevel Matrix Decomposition Algorithm (MLMDA) [24], that subdivides the MoM matrix into a large number of submatrices, operates on them separately and assembles the solutions in order to achieve faster CPU-times.…”

Fast Preconditioned Krylov Methods for Boundary Integral Equations in Electromagnetic Scattering

“…The BiCOR and CORS methods are introduced in Carpentieri et al (2011);Jing, Huang, Zhang, Li, Cheng, Ren, Duan, Sogabe & Carpentieri (2009 A significant amount of work has been devoted in the last years to design fast algorithms that can reduce the O(n 2 ) computational complexity for the M-V product operation required at each step of a Krylov method, such as the Fast Multipole Method (FMM) (Greengard & Rokhlin (1987); Rokhlin (1990)), the panel clustering method (Hackbush & Nowak (1989)), the H-matrix approach (Hackbush (1999)), wavelet techniques (Alpert et al (1993); Bond & Vavasis (1994)), the adaptive cross approximation method (Bebendorf (2000)), the impedance matrix localization method (Canning (1990)), the multilevel matrix decomposition algorithm (Michielssen & Boag (1996)) and others. In particular, the combination of iterative Krylov subspace solvers and FMM is a popular approach for solving integral equations.…”

Performance analysis of parallel Krylov methods for solving boundary integral equations in electromagnetism

“…Fertile research efforts have led in the last 20 years to the development of fast methods for performing approximate matrixvector products with boundary integral operators in O(n log n) arithmetic operations and O(n log n) memory storage (see e.g. References [5][6][7][8][9][10]), including reliable implementations on distributed memory computers [1,11]. The FMM algorithm, introduced by Greengard and Rokhlin [8,12], is a method in this class; it is approximate in the sense that the relative error in the matrix-vector computation is of the order of = 10 −3 .…”