Browsing by Subject "Integral-equation"

Now showing 1 - 3 of 3

Open Access
MLFMA solutions of transmission problems Involving realistic metamaterial walls
(IEEE, 2007-08) Ergül, Özgür; Ünal, Alper; Gürel, Levent
We present the solution of multilayer metamaterial (MM) structures containing large numbers of unit cells, such as split-ring resonators. Integral-equation formulations of scattering problems are solved iteratively by employing a parallel implementation of the multilevel fast multipole algorithm. Due to ill-conditioned nature of the problems, advanced preconditioning techniques are used to obtain rapid convergence in the iterative solutions. By constructing a sophisticated simulation environment, we accurately and efficiently investigate large and complicated MM structures. © 2007 IEEE.
Open Access
Parallel preconditioners for solutions of dense linear systems with tens of millions of unknowns
(2007-11) Malas, Tahir; Ergül, Özgür; Gürel, Levent
We propose novel parallel preconditioning schemes for the iterative solution of integral equation methods. In particular, we try to improve convergence rate of the ill-conditioned linear systems formulated by the electric-field integral equation, which is the only integral-equation formulation for targets having open surfaces. For moderate-size problems, iterative solution of the near-field system enables much faster convergence compared to the widely used sparse approximate inverse preconditioner. For larger systems, we propose an approximation strategy to the multilevel fast multipole algorithm (MLFMA) to be used as a preconditioner. Our numerical experiments reveal that this scheme significantly outperforms other preconditioners. With the combined effort of effective preconditioners and an efficiently parallelized MLFMA, we are able to solve targets with tens of millions of unknowns, which are the largest problems ever reported in computational electromagnetics. ©2007 IEEE.
Open Access
Solution of large-scale scattering problems with the multilevel fast multipole algorithm parallelized on distributed-memory architectures
(IEEE, 2007) Ergül, Özgür; Gürel, Levent
We present the solution of large-scale scattering problems involving three-dimensional closed conducting objects with arbitrary shapes. With an efficient parallelization of the multilevel fast multipole algorithm on relatively inexpensive computational platforms using distributed-memory architectures, we perform the iterative solution of integral-equation formulations that are discretized with tens of millions of unknowns. In addition to canonical problems, we also present the solution of real-life problems involving complicated targets with large dimensions.