Efficient solution of the combined-field integral equation with the parallel multilevel fast multipole algorithm

Download
2007-08-31
Gürel, Levent
Ergül, Özgür Salih
We present fast and accurate solutions of large-scale scattering problems formulated with the combined-field integral equation. Using the multilevel fast multipole algorithm (MLFMA) parallelized on a cluster of computers, we easily solve scattering problems that are discretized with tens of millions of unknowns. For the efficient parallelization of MLFMA, we propose a hierarchical partitioning scheme based on distributing the multilevel tree among the processors with an improved load-balancing. The accuracy of the solutions is demonstrated on scattering problems involving spheres of various radii from 80λ to 110λ. In addition to canonical problems, we also present the solution of real-life problems involving complicated targets with large dimensions.
2007 Computational Electromagnetics Workshop

Suggestions

Solutions of electromagnetics problems involving hundreds of millions of unknowns with parallel multilevel fast multipole algorithmt
Ergül, Özgür Salih (2009-06-05)
We present the solution of extremely large electromagnetics problems formulated with surface integral equations (SIEs) and discretized with hundreds of millions of unknowns. Scattering and radiation problems involving three-dimensional closed metallic objects are formulated rigorously by using the combined-field integral equation (CFIE). Surfaces are discretized with small triangles, on which the Rao-Wilton-Glisson (RWG) functions are defined to expand the induced electric current and to test the boundary c...
Iterative solution of the normal-equations form of the electric-field integral equation
Ergül, Özgür Salih (2007-06-15)
In this paper, we show that transforming the original equations into normal equations improves the convergence of EFIE significantly. We present the solutions of EFIE by employing the least-squares QR (LSQR) algorithm, which corresponds to a stable application of the conjugate gradient (CG) algorithm on the normal equations. Despite the squaring of the condition number due to such a transformation into the normal equations, LSQR improves the convergence rate of the iterative solutions of EFIE and performs b...
Accurate Solutions of Extremely Large Integral-Equation Problems in Computational Electromagnetics
Ergül, Özgür Salih (2013-02-01)
Accurate simulations of real-life electromagnetics problems with integral equations require the solution of dense matrix equations involving millions of unknowns. Solutions of these extremely large problems cannot be achieved easily, even when using the most powerful computers with state-of-the-art technology. However, with the multilevel fast multipole algorithm (MLFMA) and parallel MLFMA, we have been able to obtain full-wave solutions of scattering problems discretized with hundreds of millions of unknow...
Solution of large-scale scattering problems with the multilevel fast multipole algorithm parallelized on distributed-memory architectures
Ergül, Özgür Salih (2007-11-09)
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...
Improving the accuracy of the MFIE with the choice of basis functions
Ergül, Özgür Salih (2004-06-26)
In the method-of-moments (MOM) and the fast-multipole-method (FMM) solutions of the electromagnetic scattering problems modeled by arbitrary planar triangulations, the magnetic-field integral equation (MFIE) can be observed to give less accurate results compared to the electric-field integral equation (EFIE), if the current is expanded with the Rao-Wilton-Glisson (RWG) basis functions. The inaccuracy is more evident for problem geometries with sharp edges or tips. This paper shows that the accuracy of the M...
Citation Formats
L. Gürel and Ö. S. Ergül, “Efficient solution of the combined-field integral equation with the parallel multilevel fast multipole algorithm,” presented at the 2007 Computational Electromagnetics Workshop, İzmir, Turkey, 2007, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/36362.