scholarly journals A Hybrid Technique Based on the Combination of Multilevel Fast Multipole Algorithm and the Geometrical Theory of Diffraction

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
María-Jesús Algar ◽  
Javier Moreno ◽  
Iván González ◽  
Lorena Lozano ◽  
Felipe Cátedra
Keyword(s):  
Hybrid Technique ◽  
Geometrical Theory ◽  
Fast Multipole ◽  
Electromagnetic Problems ◽  
B Splines ◽  
Complex Shapes ◽  
Multilevel Fast Multipole Algorithm ◽  
Scatter Field ◽  
Geometrical Theory Of Diffraction ◽  
Fast Multipole Algorithm

This paper proposes a hybrid technique for treating electromagnetic problems of scattering and radiation in which the source structure is described as an array of antennas. This strategy is based on the combination of the rigorous method multilevel fast multipole algorithm (MLFMA) and the high frequency technique geometrical theory of diffraction (GTD). Thanks to the use of MLFMA, the source can be discretized into several cubic regions considering each of them as a source point in order to reduce the number of times required to compute the ray tracing when GTD is applied to obtain the scatter field. In this analysis, objects with complex shapes are described by using nonuniform rational B-splines (NURBS) which is a very common way to model geometrical bodies. Numerical results that demonstrate the accuracy and efficiency in terms of CPU time are shown.

scholarly journals Combining the multilevel fast multipole method with the uniform geometrical theory of diffraction

2005 ◽  
Vol 3 ◽  
pp. 183-188
Author(s):  
A. Tzoulis ◽  
T. F. Eibert
Keyword(s):  
Integral Equation ◽  
Hybrid Methods ◽  
Fast Multipole Method ◽  
Boundary Integral ◽  
Hybrid Technique ◽  
Geometrical Theory ◽  
Fast Multipole ◽  
Multipole Method ◽  
Geometrical Theory Of Diffraction ◽  
Field Integral

Abstract. The presence of arbitrarily shaped and electrically large objects in the same environment leads to hybridization of the Method of Moments (MoM) with the Uniform Geometrical Theory of Diffraction (UTD). The computation and memory complexity of the MoM solution is improved with the Multilevel Fast Multipole Method (MLFMM). By expanding the k-space integrals in spherical harmonics, further considerable amount of memory can be saved without compromising accuracy and numerical speed. However, until now MoM-UTD hybrid methods are restricted to conventional MoM formulations only with Electric Field Integral Equation (EFIE). In this contribution, a MLFMM-UTD hybridization for Combined Field Integral Equation (CFIE) is proposed and applied within a hybrid Finite Element - Boundary Integral (FEBI) technique. The MLFMM-UTD hybridization is performed at the translation procedure on the various levels of the MLFMM, using a far-field approximation of the corresponding translation operator. The formulation of this new hybrid technique is presented, as well as numerical results.

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