Revision of wFMM ?A Wideband Fast Multipole Method for the two-dimensional complex Helmholtz equation

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• 作者：Min Hyung Cho ;   ; ^{mhcho@uncc.edu} ; Wei Cai ;   ; ^{wcai@uncc.edu}
• 关键词：Wideband Fast Multipole Method ; Helmholtz equation ; Fast solver
• 刊名：Computer Physics Communications
• 出版年：2012
• 出版时间：February 2012
• 年：2012
• 卷：183
• 期：2
• 页码：446-447
• 全文大小：94 K

文摘

The Wideband Fast Multipole Method for the two-dimensional complex Helmholtz equation program is updated. The new version uses significantly less memory than the original version and uses almost constant memory for all the wavenumbers k when the number of particles is given. The CPU time is also improved slightly. Additionally, the memory leak problems and errors from external variables when it is used in an iterative solver are fixed. The new version wFMM and other useful codes are available from the website .

New version program summary

Manuscript Title: Revision of wFMM ?A Wideband Fast Multipole Method for the two-dimensional complex Helmholtz equation

Authors: Min Hyung Cho and Wei Cai

Program Title: 2D-WFMM

Journal Reference:

Catalogue identifier: AEHI_v2_0

Program summary URL:

Program obtainable from: CPC Program Library, Queen?s University, Belfast, N. Ireland

Licensing provisions: Standard CPC licence,

No. of lines in distributed program, including test data, etc.: 4669

No. of bytes in distributed program, including test data, etc.: 46?49

Programming language: C

Computer: Any

Operating system: Any operating system with gcc compiler. For the multi-thread computing, the gcc version 4.4 or newer is recommended

RAM: Depending on the number of particles N and wavenumber k

Number of processors used: Multi-core processors with shared memory

Keywords: Wideband Fast Multipole Method, Helmholtz equation, Fast solver

Classification: 4.8, 4.12

External routines/libraries: OpenMP ()

Subprograms used: None

Catalogue identifier of previous version: AEHI_v1_0

Journal reference of previous version: Computer Physics Communications 181 (12) (2010) 2086

Does the new version supersede the previous version?: Yes

Nature of problem: Evaluate the interaction between N particles governed by the fundamental solution of 2D complex Helmholtz equation with wide range of wavenumber k.

Solution method: Multilevel Fast Multipole Algorithm in a hierarchical quad-tree data structure with a cutoff level, which combines low frequency method and high frequency method.

Reasons for the new version: Improve the efficiency of the program including memory usage, repeated use in an iterative solver or other programs, and a minor speed up.

in a box, tree depth = 6
k	Cutoff	Error	Memory (MB)	CPU time (s)
New	Old	New	Old	Direct
	1	1.71E?7	364	967	34	42	7840
	1	3.81E?7	364	961	35	41	7350
0.1	1	6.08E?8	364	1024	48	64	6860
0.2	2	2.70E?7	364	1072	48	65	7840
0.3	2	7.76E?7	363	1084	51	69	8820
0.4	3	1.15E?6	364	1013	48	66	9310
0.5	3	4.19E?7	364	1046	51	71	9310
0.6	3	1.23E?6	364	1105	51	71	9310
0.7	4	1.34E?6	363	1018	49	66	9310
0.8	4	1.10E?6	363	1047	48	66	9800
0.9	4	1.78E?6	363	1039	49	66	9800
1	4	6.00E?7	363	1106	51	71	9310
2	5	4.80E?7	363	1086	54	71	9310
5	6	6.64E?7	363	1748	65	68	9800
10	6	2.63E?7	364	1989	99	103	9800
50	6	2.59E?8	448	5756	1146	1165	9800