Modified Dual-Level Fast Multipole Algorithm Based on the Burton-Miller Formulation for Large- Scale Sound Field Analysis

2021 ◽  
pp. 91-108
Author(s):  
Jun-Pu Li ◽  
Qing-Hua Qin
Keyword(s):  
Large Scale ◽  
Sound Field ◽  
Field Analysis ◽  
Fast Multipole ◽  
Fast Multipole Algorithm

A TECHNIQUE FOR PLANE-SYMMETRIC SOUND FIELD ANALYSIS IN THE FAST MULTIPOLE BOUNDARY ELEMENT METHOD

2005 ◽  
Vol 13 (01) ◽  
pp. 71-85 ◽  
Author(s):  
Y. YASUDA ◽  
T. SAKUMA
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Large Scale ◽  
Numerical Study ◽  
Sound Field ◽  
Field Analysis ◽  
Fast Multipole ◽  
Plane Symmetric ◽  
Sound Fields ◽  
Element Method

The fast multipole boundary element method (FMBEM) is an advanced BEM, with which both the operation count and the memory requirements are O(Na log b N) for large-scale problems, where N is the degree of freedom (DOF), a ≥ 1 and b ≥ 0. In this paper, an efficient technique for analyses of plane-symmetric sound fields in the acoustic FMBEM is proposed. Half-space sound fields where an infinite rigid plane exists are typical cases of these fields. When one plane of symmetry is assumed, the number of elements and cells required for the FMBEM with this technique are half of those for the FMBEM used in a naive manner. In consequence, this technique reduces both the computational complexity and the memory requirements for the FMBEM almost by half. The technique is validated with respect to accuracy and efficiency through numerical study.

AN EFFECTIVE SETTING OF HIERARCHICAL CELL STRUCTURE FOR THE FAST MULTIPOLE BOUNDARY ELEMENT METHOD

2005 ◽  
Vol 13 (01) ◽  
pp. 47-70 ◽  
Author(s):  
Y. YASUDA ◽  
T. SAKUMA
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Large Scale ◽  
Numerical Study ◽  
Cell Structure ◽  
Sound Field ◽  
Field Analysis ◽  
Fast Multipole ◽  
Simple Method ◽  
Element Method

The fast multipole boundary element method (FMBEM) is an advanced BEM that leads to drastic reduction of processing time and memory requirements in a large-scale steady-state sound field analysis. In the FMBEM, hierarchical cell structure is employed to apply multipole expansion in multiple levels, and the setting of the hierarchical cell structure considerably affects the computational efficiency of the FMBEM. This paper deals with effective settings of hierarchical cell structure for taking full advantage of the FMBEM. A numerical study with objects of different shapes with the same DOF shows that both the computational complexity and the memory requirements with the FMBEM were greater for 1D-shaped objects than for 2D- or 3D-shaped ones, without a special setting of hierarchical cell structure for each problem. An effective setting for 1D-shaped objects is derived through theoretical and numerical studies, where special considerations are given to the arrangement of the cell structure and the treatment of translation coefficients between cells. This setting allows for efficient calculations not dependent on the shape of an analyzed object. A simple method to arrange hierarchical cell structure is proposed, which realizes the derived setting for arbitrarily-shaped problems.

Inplementation of an Efficient Parallel Multilevel Fast Multipole Algorithm

2012 ◽  
Vol 433-440 ◽  
pp. 4268-4272
Author(s):  
You Feng Chen ◽  
Dong Lin Su ◽  
Xiao Ying Zhao ◽  
Dan Dan Guo ◽  
Li Peng Deng
Keyword(s):  
Shared Memory ◽  
High Frequency ◽  
Large Scale ◽  
Memory System ◽  
Method Of Moment ◽  
Fast Multipole ◽  
Multilevel Fast Multipole Algorithm ◽  
Shared Memory System ◽  
Fast Multipole Algorithm

This paper is concerned with the implementation of the parallel multilevel fast multipole algorithm(MLFMA) for large scale electromagnetics simulation on shared-memory system. The algorithm is implemented on a method of moment discretisation of the electromagnetics scattering problems.The developed procesure is validated by compared to benchmarks defined by Electromagnetics Code Consortium(EMCC) .The procesure can evaluate large problemssuch as electromagnetics scattering of aircraft at high-frequency with up to several millions of unknowns.

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