Browsing by Subject "Large-scale systems"

Now showing 1 - 3 of 3

Open Access
Fast and accurate solutions of large-scale scattering problems with parallel multilevel fast multipole algorithm
(IEEE, 2007) Ergül, Özgür; Gürel, Levent
Fast and accurate solution of large-scale scattering problems obtained by integral-equation formulations for conducting surfaces is considered in this paper. By employing a parallel implementation of the multilevel fast multipole algorithm (MLFMA) on relatively inexpensive platforms. Specifically, the solution of a scattering problem with 33,791,232 unknowns, which is even larger than the 20-million unknown problem reported recently. Indeed, this 33-million-unknown problem is the largest integral-equation problem solved in computational electromagnetics.
Open Access
Scalable parallelization of the sparse-approximate-inverse (SAl) preconditioner for the solution of large-scale integral-equation problems
(IEEE, 2009-06) Malas, Tahir; Gürel, Levent
In this paper, we consider efficient parallelization of the sparse approximate inverse (SAI) preconditioner in the context of the multilevel fast multipole algorithm (MLFMA). Then, we report the use of SAI in the solution of very large EFIE problems. The SAI preconditioner is important not only because it is a robust preconditioner that renders many difficult and large problems solvable, but also it can be utilized for the construction of more effective preconditioners.
Open Access
Sequential and parallel preconditioners for large-scale integral-equation problems
(IEEE, 2007) Malas, Tahir; Ergül, Özgür; Gürel, Levent
For efficient solutions of integral-equation methods via the multilevel fast multipole algorithm (MLFMA), effective preconditioners are required. In this paper we review appropriate preconditioners that have been used for sparse systems and developed specially in the context of MLFMA. First we review the ILU-type preconditioners that are suitable for sequential implementations. We can make these preconditioners robust and efficient for integral-equation methods by making appropriate selections and by employing pivoting to suppress the instability problem. For parallel implementations, the sparse approximate inverse or the iterative solution of the near-field system enables fast convergence up to certain problem sizes. However, for very large problems, the near-field matrix itself becomes insufficient to approximate the dense system matrix and preconditioners generated from the near-field interactions cannot be effective. Therefore, we propose an approximation strategy to MLFMA to be used as an effective 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 problems with tens of millions of unknowns in a few hours. We report the solution of integral-equation problems that are among the largest in their classes. © 2007 IEEE.