AIM - ADAPTIVE INTEGRAL METHOD FOR SOLVING LARGE-SCALE ELECTROMAGNETIC SCATTERING AND RADIATION PROBLEMS

We describe basic elements and implementation of the adaptive integral method (AIM): a fast iterative integral-equation solver applicable to large-scale electromagnetic scattering and radiation problems. As com pared to the conventional method of moments, the AIM solver provides ( for typical geometries) significantly reduced storage and solution tim e already for problems involving 2,000 unknowns. This reduction is ach ieved through a compression of the impedance matrix, split into near-f ield and far-field components. The near-field component is computed by using the Galerkin method employing a set of N arbitrary basis functi ons. The far-field matrix elements are calculated by using the Galerki n method as well, with a set of N auxiliary basis functions. The auxil iary basis functions are constructed as superpositions of pointlike cu rrent elements located on uniformly spaced Cartesian grid nodes and ar e required to reproduce, with a prescribed accuracy, the far field gen erated by the original basis functions. Algebraically, the resulting n ear-field component of the impedance matrix is sparse, while its far-f ield component is a product of two sparse matrices and a three-level T oeplitz matrix. These Toeplitz properties are exploited, by using disc rete fast Fourier transforms, to carry out matrix-vector multiplicatio ns with O(N(3/2)logN) and O(NlogN) serial complexities for surface and volumetric scattering problems, respectively. The corresponding stora ge requirements are O(N-3/2) and O(N). In the domain-decomposed parall elized implementation of the solver, with the number Np of processors equal to the number of domains, the total memory required in surface p roblems is reduced to O(N-3/2/N-p(1/2)). The speedup factor in matrix- vector multiplication is equal to the number of processors N-p. We pre sent a detailed analysis of the errors introduced by the use of the au xiliary basis functions in computing far-field impedance matrix elemen ts. We also discuss the algorithm complexity and some aspects of its i mplementation and applications.