Fast Multipole Boundary Element Method (FastBEM) Software

for Education, Research and Further Development

Dr. Yijun Liu, CAE Research Lab, University of Cincinnati, Ohio, USA

 

The fast multipole method (FMM), pioneered by Rokhlin and Greengard in the mid of 1980's, can be employed to dramatically accelerate the solution of a BEM system of equations Ax = b, in which matrix A is in general dense and non-symmetrical. The main idea of the fast multipole BEM is to employ iterative solvers (such as GMRES) to solve the BEM system of equations and employ the FMM to accelerate the matrix-vector multiplication (Ax) in each iteration step, without ever forming the matrix A explicitly. In the fast multipole BEM, the node-to-node interactions in the conventional BEM are replaced by cell-to-cell interactions using a hierarchical tree structure of cells containing groups of elements. This is possible by introducing the multipole and local expansions of the kernels and employing certain translations. For more information about the fast multipole BEM, please read a comprehensive review: N. Nishimura, "Fast multipole accelerated boundary integral equation methods," Appl. Mech. Rev., 55, 299-324 (2002); or the first textbook: Y. J. Liu, Fast Multipole Boundary Element Method - Theory and Applications in Engineering, Cambridge University Press, Cambridge (2009).

Some Unique Applications of the Fast Multipole BEM Software

(Click on the pictures to see larger images)

A. Thermal Analysis:  Fuel Cells

(There are 9,000 small side holes in this model! Total DOFs = 530,000, solved on a desktop PC)

B. Elasticity:  Fiber Composites

(Up to 16,000 CNT fibers and total DOFs = 28,800,000, solved on a supercomputer at Kyoto University)

C. Stokes Flow:  MEMS

(This is an exterior Stokes flow problem. Total DOFs = 1,087,986, solved on a desktop PC)

D. Acoustics:  Noise Control

(This is an exterior acoustic wave radiation problem. Total complex DOFs = 541,152, solved on a desktop PC)

Fast Multipole BEM Software Packages for Download

Release Update (September 22, 2014): 2-D Acoustics package is updated to correct an error in the code when using the dual BIE formulation.

The following fast multipole boundary element method (FastBEM) software packages (for Windows OS only) are provided for free download and non-commercial use for the sole purpose of promoting the education, research and further development of the fast multipole BEM. Bug reports of the software and suggestions for improvements are most welcome. If you wish to collaborate and develop new capabilities for the fast multipole BEM applications, please contact Dr. Liu. See also the Copyright Statement.

Program

Description and References

Download

Examples

A1. FastBEM

2-D Potential

A fast multipole boundary element code for solving general 2-D potential problems governed by the Laplace equation, including thermal and electrostatic problems, using the dual BIE formulation (α CBIE + β HBIE).

References: Chapter 3 of Ref. [1], and Refs. [2-3].

Package A1

(Updated 1/14/2014)

 

Source code used in Refs. [1] and [2]

Porous material and MEMS

A2. FastBEM

3-D Potential

A fast multipole boundary element code for solving general 3-D potential problems governed by the Laplace equation, including thermal and electrostatic problems, using the dual BIE formulation (α CBIE + β HBIE).

References: Chapter 3 of Ref. [1], and Refs. [4-5, 15].

Package A2

(Updated 1/14/2014)

Heat conduction and electrostatics

B1. FastBEM

2-D Elasticity

A fast multipole boundary element code for solving general 2-D linear elasticity problems with homogeneous and isotropic materials.

References: Chapter 4 of Ref. [1], and Refs. [6-7].

Package B1

(Updated 1/14/2014)

Porous and honeycomb materials

B2. FastBEM

3-D Elasticity

A fast multipole boundary element code for solving general 3-D linear elasticity problems with homogeneous and isotropic materials.

References: Chapter 4 of Ref. [1], and Refs. [8-10].

Package B2

(Updated 1/14/2014)

Composites and scaffold materials

C1. FastBEM

2-D Stokes Flow

A fast multipole boundary element code for solving general 2-D Stokes flow problems using the dual direct BIE formulation (α CBIE + β HBIE).

References: Chapter 5 of Ref. [1], and Ref. [11].

Package C1

(Updated 1/14/2014)

2-D Stokes flows

C2. FastBEM

3-D Stokes Flow

A fast multipole boundary element code for solving general 3-D Stokes flow problems using the direct BIE formulation.

References: Chapter 5 of Ref. [1].

Package C2

(Updated 1/14/2014)

 

3-D Stokes flows

D1. FastBEM

2-D Acoustics

An adaptive fast multipole boundary element code for solving general 2-D acoustic wave problems governed by the Helmholtz equation using the dual BIE formulation (α CBIE + β HBIE).

References: Chapter 6 of Ref. [1], and Ref. [12].

Package D1

(Updated 9/22/2014)

2-D radiation and scattering

D2. FastBEM

3-D Acoustics

An adaptive fast multipole boundary element code for solving general 3-D acoustic wave problems governed by the Helmholtz equation using the dual BIE formulation (α CBIE + β HBIE).

References: Chapter 6 of Ref. [1], and Refs. [12-15].

Visit www.fastbem.com to download the commercial program

3-D radiation and scattering

References:

  1. Y. J. Liu, Fast Multipole Boundary Element Method - Theory and Applications in Engineering, Cambridge University Press, Cambridge (2009).

  2. Y. J. Liu and N. Nishimura, "The fast multipole boundary element method for potential problems: a tutorial,"  Engineering Analysis with Boundary Elements30, No. 5, 371-381 (2006). (Corrected Figures 4 and 5)

  3. Y. J. Liu, "Dual BIE approaches for modeling electrostatic MEMS problems with thin beams and accelerated by the fast multipole method,"  Engineering Analysis with Boundary Elements, 30, No. 11, 940-948 (2006).

  4. L. Shen and Y. J. Liu, "An adaptive fast multipole boundary element method for three-dimensional potential problems,"  Computational Mechanics,  39, No. 6, 681-691 (2007).

  5. Y. J. Liu and L. Shen, "A dual BIE approach for large-scale modeling of 3-D electrostatic problems with the fast multipole boundary element method,"  International Journal for Numerical Methods in Engineering, 71, No. 7, 837855, (2007).

  6. Y. J. Liu, "A new fast multipole boundary element method for solving large-scale two-dimensional elastostatic problems,"  International Journal for Numerical Methods in Engineering, 65, No. 6, 863-881 (2006).

  7. Y. J. Liu, "A fast multipole boundary element method for 2-D multi-domain elastostatic problems based on a dual BIE formulation,"  Computational Mechanics, 42, No. 5, 761-773 (2008).

  8. Y. J. Liu, N. Nishimura, Y. Otani, T. Takahashi, X. L. Chen and H. Munakata, "A fast boundary element method for the analysis of fiber-reinforced composites based on a rigid-inclusion model," ASME Journal of Applied Mechanics, 72, No. 1, 115-128 (2005).

  9. Y. J. Liu, N. Nishimura and Y. Otani, "Large-scale modeling of carbon-nanotube composites by a fast multipole boundary element method,"  Computational Materials Science34, No. 2, 173-187 (2005).

  10. Y. J. Liu, N. Nishimura, D. Qian, N. Adachi, Y. Otani and V. Mokashi, "A boundary element method for the analysis of CNT/polymer composites with a cohesive interface model based on molecular dynamics,"  Engineering Analysis with Boundary Elements32, No. 4, 299308 (2008).

  11. Y. J. Liu, "A new fast multipole boundary element method for solving 2-D Stokes flow problems based on a dual BIE formulation,"  Engineering Analysis with Boundary Elements32, No. 2, 139-151 (2008).

  12. Y. J. Liu, L. Shen and M. Bapat, "Development of the Fast Multipole Boundary Element Method for Acoustic Wave Problems," in: Recent Advances in the Boundary Element Methods, edited by G. Manolis and D. Polyzos (Springer-Verlag, Berlin, 2009).

  13. L. Shen and Y. J. Liu, "An adaptive fast multipole boundary element method for three-dimensional acoustic wave problems based on the Burton-Miller formulation,"  Computational Mechanics, 40, No. 3, 461-472 (2007).

  14. M. S. Bapat, L. Shen and Y. J. Liu, "Adaptive fast multipole boundary element method for three-dimensional half-space acoustic wave problems,"  Engineering Analysis with Boundary Elements33, Nos. 8-9, 1113-1123 (2009).

  15. M. S. Bapat and Y. J. Liu, "A new adaptive algorithm for the fast multipole boundary element method,"  CMES: Computer Modeling in Engineering & Sciences, 58, No. 2, 161-184 (2010).

2004-2014. Copyright Notice and Disclaimers:

The above fast multipole boundary element method (FastBEM) software packages are copyrighted materials of the authors. No part of the packages, either the executable or the source codes, can be used for any commercial applications and distributions without prior written permissions of the original authors. Proper acknowledgment should be given in publications resulting from the use of these software. The authors retain all the rights of these software. There is no warranty, expressed or implied, for the use of these software. The authors are not responsible for any possible damages in using these software and no technical support is available to users of these software.

 

 

Dr. Yijun Liu

Mechanical Engineering

University of Cincinnati, P.O. Box 210072

Cincinnati, OH 45221-0072, U.S.A.

Tel.:         (513) 556-4607 (Voice),    (513) 556-3390 (Fax)

E-mail:    Yijun.Liu@uc.edu
Web:        www.yijunliu.com

Site accessed  times since January 15, 2007.

  1996-2014 Yijun Liu, University of Cincinnati

 

Last updated:   January 14, 2014.