Surface Integral Equation Solutions by Hierarchical Vector Basis Functions and Spherical Harmonics Based Multilevel Fast Multipole Method

2009 ◽  
Vol 57 (7) ◽  
pp. 2084-2093 ◽  
Author(s):  
Ismatullah ◽  
T.F. Eibert
Keyword(s):  
Integral Equation ◽  
Spherical Harmonics ◽  
Fast Multipole Method ◽  
Basis Functions ◽  
Fast Multipole ◽  
Surface Integral ◽  
Surface Integral Equation ◽  
Vector Basis ◽  
Multipole Method

Application of higher-order vector basis functions to surface integral equation formulations

Radio Science ◽  
1996 ◽  
Vol 31 (5) ◽  
pp. 1207-1213 ◽  
Author(s):  
Keith R. Aberegg ◽  
Atsuo Taguchi ◽  
Andrew F. Peterson
Keyword(s):  
Integral Equation ◽  
Higher Order ◽  
Basis Functions ◽  
Surface Integral ◽  
Surface Integral Equation ◽  
Vector Basis

scholarly journals The Application of Improved Spherical Harmonics Expansion-Based Multilevel Fast Multipole Algorithm in the Solution of Volume-Surface Integral Equation

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Jinbo Liu ◽  
Mang He ◽  
Zengrui Li ◽  
Jianxun Su
Keyword(s):  
Integral Equation ◽  
Spherical Harmonics ◽  
Hardware Acceleration ◽  
Memory Requirement ◽  
Fast Multipole ◽  
Surface Integral ◽  
Surface Integral Equation ◽  
Multilevel Fast Multipole Algorithm ◽  
Spherical Harmonics Expansion ◽  
Fast Multipole Algorithm

During the solution of volume-surface integral equation (VSIE), to reduce the core memory requirement of the radiation patterns (RPs) of the basis functions, an improved spherical harmonics expansion-based multilevel fast multipole algorithm (SE-MLFMA) using the mixed-potential representation and the triangle-/tetrahedron-based grouping scheme is applied. Numerical results show that accompanying with a faster speed, the memory requirement of the RPs in the improved SE-MLFMA is several times less than that in the conventional MLFMA without compromising accuracy. A result employing the OpenMP parallelization and vector arithmetic logic unit (VALU) hardware acceleration technique is also shown to illustrate the robustness and scalability of the improved SE-MLFMA method.

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