Browsing by Subject "Large-scale problem"

Now showing 1 - 7 of 7

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
Accuracy: The Frequently Overlooked Parameter in the Solution of Extremely Large Problems
(IEEE, 2011) Ergul, O.; Gürel, Levent
We investigate error sources and their effects on the accuracy of solutions of extremely large electromagnetics problems with parallel implementations of the multilevel fast multipole algorithm (MLFMA). Accuracy parameters and their effects on the accuracy of MLFMA solutions are studied for large-scale problems discretized with hundreds of millions of unknowns. We show that some error sources are more dominant and should be suppressed for more accurate solutions; identifying less-effective error sources may allow us to derive more efficient implementations. Based on our analysis, we determine a set of benchmark problems that can be used to compare the accuracy of solvers for large-scale computations. A benchmarking tool is provided at www.cem.bilkent.edu.tr/ benchmark.
Open Access
Broadband multilevel fast multipole algorithm for large-scale problems with nonuniform discretizations
(IEEE, 2016) Ergül, Ö.; Karaosmanoğlu, B.; Takrimi, Manouchehr; Ertürk, Vakur B.
We present a broadband implementation of the multilevel fast multipole algorithm (MLFMA) for fast and accurate solutions of multiscale problems involving highly nonuniform discretizations. Incomplete tree structures, which are based on population-based clustering with flexible leaf-level boxes at different levels, are used to handle extremely varying triangulation sizes on the same structures. Superior efficiency and accuracy of the developed implementation, in comparison to the standard and broadband MLFMA solvers employing conventional tree structures, are demonstrated on practical problems.
Open Access
Fast and accurate solutions of extremely large scattering problems involving three-dimensional canonical and complicated objects
(IEEE, 2009-07) Ergül, Özgür; Gürel, Levent
We present fast and accurate solutions of extremely large scattering problems involving three-dimensional metallic objects discretized with hundreds of millions of unknowns. Solutions are performed by the multilevel fast multipole algorithm, which is parallelized efficiently via a hierarchical partition strategy. Various examples involving canonical and complicated objects are presented in order to demonstrate the feasibility of accurately solving large-scale problems on relatively inexpensive computing platforms without resorting to approximation techniques. ©2009 IEEE.
Open Access
MLFMA memory reduction techniques for solving large-scale problems
(IEEE, 2014) Hidayetoğlu, Mert; Gürel, Levent
We present two memory reduction methods for the parallel multilevel fast multipole algorithm. One of these methods uses data structures out of core, and the other parallelizes the data structures related to input geometry. With these methods, large-scale electromagnetic scattering problems can be solved on modest parallel computers. © 2014 IEEE.
Open Access
Parallel-MLFMA solutions of large-scale problems involving composite objects
(IEEE, 2012-07) Ergül, Özgür; Gürel, Levent
We present a parallel implementation of the multilevel fast multipole algorithm (MLFMA) for fast and accurate solutions of large-scale electromagnetics problems involving composite objects with dielectric and metallic parts. Problems are formulated with the electric and magnetic current combined-field integral equation (JMCFIE) and solved iteratively with MLFMA on distributed-memory architectures. Numerical examples involving canonical and complicated objects, such as optical metamaterials, are presented to demonstrate the accuracy and efficiency of the implementation. © 2012 IEEE.
Open Access
Rigorous solutions of large-scale dielectric problems with the parallel multilevel fast multipole algorithm
(IEEE, 2011) Ergül, Özgür; Gürel, Levent
We present fast and accurate solutions of large-scale electromagnetics problems involving three-dimensional homogeneous dielectric objects. Problems are formulated rigorously with the electric and magnetic current combined-field integral equation (JMCFIE) and solved iteratively with the multilevel fast multipole algorithm (MLFMA). In order to solve large-scale problems, MLFMA is parallelized efficiently on distributed-memory architectures using the hierarchical partitioning strategy. Efficiency and accuracy of the developed implementation are demonstrated on very large scattering problems discretized with tens of millions of unknowns. © 2011 IEEE.