The fast multipole method for the symmetric boundary integral formulation

2006 ◽  
Vol 26 (2) ◽  
pp. 272-296 ◽  
Author(s):  
G. Of ◽  
O. Steinbach ◽  
W.L. Wendland
Keyword(s):  
Fast Multipole Method ◽  
Boundary Integral ◽  
Integral Formulation ◽  
Fast Multipole ◽  
Boundary Integral Formulation ◽  
Multipole Method

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.

Scattering by cracks in a conducting surface

2020 ◽  
Vol 39 (3) ◽  
pp. 709-723
Author(s):  
Ralf T. Jacobs ◽  
Arnulf Kost
Keyword(s):  
Fast Multipole Method ◽  
Boundary Integral ◽  
Fast Multipole ◽  
Scattering Problems ◽  
Group Interactions ◽  
Content Type ◽  
Conventional Procedure ◽  
Incident Plane ◽  
Convolution Algorithm ◽  
Multipole Method

Purpose The purpose of this study is the formulation of an efficient method to compute and analyse the scattering characteristics of cracks or grooves in a conducting object, where the size of the crack is significantly larger than the wavelength of an incident plane wave. Design/methodology/approach A hybrid finite element-boundary element procedure is formulated for the computation of the scattering properties of the object, where the fast multipole method is used in the boundary integral formulation. The basic fast multipole procedure is enhanced by utilising a fast Fourier transform-based convolution algorithm for the computation of the interactions between groups of source and field elements. Findings The algorithm accelerates the evaluation of the group interactions and enables the reduction of the memory requirements without introducing an additional approximation into the procedure. Originality/value The fast multipole method with convolution algorithm shows to be more efficient for the computation of scattering problems with a large number of unknowns than the conventional procedure.

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