Open problems in CEM

This work provides an overview of a parallel, high-order, error-controllable framework for solving large-scale scattering problems in electromagnetics, as well as open problems pertinent to such solutions. The method is based on the higherorder locally corrected Nystrom (LCN) discretization of the combined-field integral equation (CFIE), accelerated with the error-controlled Multi-Level Fast Multipole Algorithm (MLFMA). Mechanisms for controlling the accuracy of calculations are discussed, including geometric representation, stages of the locally corrected Nystrom method, and the MLFMA. Also presented are the key attributes of parallelization for the developed numerical framework. Numerical results validate the proposed numerical scheme by demonstrating higher-order error convergence for smooth scatterers. For the problem of scattering from a sphere, the developed numerical solution is shown to have the ability to produce a solution with a maximum relative error of the order 10-9. Open-ended problems, such as treatment of general scatterers with geometric singularities, construction of well-conditioned operators, and current challenges in development of fast iterative and direct algorithms, are also discussed.
IEEE Antennas and Propagation Magazine


Fast-Multipole-Method Solutions of New Potential Integral Equations
Gür, Uğur Meriç; Karaosmanoglu, Bariscan; Ergül, Özgür Salih (2017-09-27)
A recently introduced potential integral equations for stable analysis of low-frequency problems involving dense discretizations with respect to wavelength are solved by using the fast multipole method (FMM). Two different implementations of FMM based on multipoles and an approximate diagonalization employing scaled plane waves are developed and used for rigorous solutions of low-frequency problems. Numerical results on canonical problems demonstrate excellent stability and solution capabilities of both imp...
Ergül, Özgür Salih (2011-01-01)
We present a parallel implementation of the multilevel fast multipole algorithm (MLFMA) for fast and accurate solutions of electromagnetics problems involving homogeneous objects with diverse material properties. Problems are formulated rigorously with the electric and magnetic current combined-field integral equation (JMCFIE) and solved iteratively using MLFMA parallelized with the hierarchical partitioning strategy. Accuracy and efficiency of the resulting implementation are demonstrated on canonical prob...
Efficient preconditioning strategies for the multilevel fast multipole algorithm
Gurel, Levent; Malas, Tahir; Ergül, Özgür Salih (2007-03-30)
For the iterative solutions of the integral equation methods employing the multilevel fast multipole algorithm (MLFMA), effective preconditioning techniques should be developed for robustness and efficiency. Preconditioning techniques for such problems can be broadly classified as fixed preconditioners that are generated from the sparse near-field matrix and variable ones that can make use of MLFMA with the help of the flexible solvers. Among fixed preconditioners, we show that an incomplete LU precondition...
Parallel linear solution of large structures on heterogeneous PC clusters
Kurç, Özgür (2006-12-01)
In this paper, a parallel solution framework for the linear static analysis of large structures on heterogeneous PC clusters is presented. The framework consists of two main steps; data preparation and parallel solution. The parallel solution is performed by a substructure based method with direct solvers. The aim of the data preparation step is to create the best possible substructures so that the condensation times of substructures are balanced. Examples which illustrate the applicability and the efficien...
Broadband Analysis of Multiscale Electromagnetic Problems: Novel Incomplete-Leaf MLFMA for Potential Integral Equations
Khalichi, Bahram; Ergül, Özgür Salih; Takrimi, Manouchehr; Erturk, Vakur B. (2021-12-01)
Recently introduced incomplete tree structures for the magnetic-field integral equation are modified and used in conjunction with the mixed-form multilevel fast multipole algorithm (MLFMA) to employ a novel broadband incomplete-leaf MLFMA (IL-MLFMA) to the solution of potential integral equations (PIEs) for scattering/radiation from multiscale open and closed surfaces. This population-based algorithm deploys a nonuniform clustering that enables to use deep levels safely and, when necessary, without compromi...
Citation Formats
Ö. S. Ergül, “Open problems in CEM,” IEEE Antennas and Propagation Magazine, pp. 294–294, 2013, Accessed: 00, 2020. [Online]. Available: