Browsing by Subject "Problem size"

Now showing 1 - 3 of 3

Open Access
Accuracy and efficiency considerations in the solution of extremely large electromagnetics problems
(IEEE, 2011) Gürel, Levent; Ergül, Özgür
This study considers fast and accurate solutions of extremely large electromagnetics problems. Surface formulations of large-scale objects lead to dense matrix equations involving millions of unknowns. Thanks to recent developments in parallel algorithms and high-performance computers, these problems can easily be solved with unprecedented levels of accuracy and detail. For example, using a parallel implementation of the multilevel fast multipole algorithm (MLFMA), we are able to solve electromagnetics problems discretized with hundreds of millions of unknowns. Unfortunately, as the problem size grows, it becomes difficult to assess the accuracy and efficiency of the solutions, especially when comparing different implementations. This paper presents our efforts to solve extremely large electromagnetics problems with an emphasis on accuracy and efficiency. We present a list of benchmark problems, which can be used to compare different implementations for large-scale problems. © 2011 IEEE.
Open Access
Effective preconditioners for large integral-equation problems
(IET, 2007-11) Malas, Tahir; Ergül, Özgür; Gürel, Levent
We consider effective preconditioning schemes for the iterative solution of integral-equation methods. 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 too crude approximation to the dense system matrix and preconditioners generated from the near-field interactions cannot be effective. Therefore, 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 in a few hours.
Open Access
Improving iterative solutions of the electric-field integral equation via transformations into normal equations
(Taylor and Francis, 2012-04-03) Ergül, Özgür; Gürel, Levent
We consider the solution of electromagnetics problems involving perfectly conducting objects formulated with the electric-field integral equation (EFIE). Dense matrix equations obtained from the discretization of EFIE are solved iteratively by the generalized minimal residual (GMRES) algorithm accelerated with a parallel multilevel fast multipole algorithm. We show that the number of iterations is halved by transforming the original matrix equations into normal equations. This way, memory required for the GMRES algorithm is reduced by more than 50%, which is significant when the problem size is large.