Based on the different characteristics of memory requirement and CPU time at different levels in the Multi-Level Fast Multipole Algorithm (MLFMA), a new highly efficient parallel approach is proposed, which employs different techniques to parallelize the plane waves and translation matrices at different levels. The formulae for efficiently implementing this proposed approach are presented by theoretical analysis and numerical experiments. Several techniques have also been employed to reduce memory requirement. The proposed parallel approach is implemented and investigated numerically, showing that the proposed approach is very accurate and efficient. The radar cross-section (RCS) of a conducting sphere with a diameter of 144λ (wavelength), simulated by over 10 millions unknowns, is successfully computed in the Center for Electromagnetic Simulation (CEMS) in the Beijing Institute of Technology (BIT), demonstrating the strong computation power of this proposed approach. The comparison of numerical performance between Center for Computation Electromagnetics (CCEM) in University of Illinois at Urbana-Champaign (UIUC) and our CEMS is also presented in this paper.
Abstract-An efficient higher order MLFMA is developed by using an "extended-tree". With this extended-tree, the size of the box at the finest level is reduced, and the cost associated with the aggregation and disaggregation operations is significantly decreased. The sparse approximate inverse (SAI) preconditioner is utilized to accelerate the convergence of iterative solutions. The Cholesky factorization, instead of the often used QR factorization, is employed to construct the SAI preconditioner for cavity scattering analysis, by taking advantage of the symmetry of the matrix arising from electric field integral equation. Numerical experiments show that the higher order MLFMA is more efficient than its low-order counterpart.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.