A new simple multidomain fast multipole boundary element method
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A simple multidomain fast multipole boundary element method (BEM) for solving potential problems is presented in this paper, which can be applied to solve a true multidomain problem or a large-scale single domain problem using the domain decomposition technique. In this multidomain BEM, the coefficient matrix is formed simply by assembling the coefficient matrices of each subdomain and the interface conditions between subdomains without eliminating any unknown variables on the interfaces. Compared with other conventional multidomain BEM approaches, this new approach is more efficient with the fast multipole method, regardless how the subdomains are connected. Instead of solving the linear system of equations directly, the entire coefficient matrix is partitioned and decomposed using Schur complement in this new approach. Numerical results show that the new multidomain fast multipole BEM uses fewer iterations in most cases with the iterative equation solver and less CPU time than the traditional fast multipole BEM in solving large-scale BEM models. A large-scale fuel cell model with more than 6 million elements was solved successfully on a cluster within 3 h using the new multidomain fast multipole BEM.
KeywordsMultidomain problems Domain decomposition Boundary element method Fast multipole method
The authors would like to acknowledge the support of Ohio Supercomputer Center (OSC). All the computing jobs for the examples were done on the “Oakley” cluster at OSC.
- 18.Sarradj E (2003) Multi-domain boundary element method for sound fields in and around porous absorbers. Acta Acust United Acust 89(1):21–27Google Scholar
- 26.Florez WF, Power H (2001) Comparison between continuous and discontinuous boundary elements in the multidomain dual reciprocity method for the solution of the two-dimensional Navier-Stokes equations. Eng Anal Bound Elem 25(1):57–69. doi: 10.1016/S0955-7997(00)00051-5 MathSciNetCrossRefMATHGoogle Scholar
- 31.Kane JH, Kashava Kumar BL, Saigal S (1990) An arbitrary condensing, noncondensing solution strategy for large scale, multi-zone boundary element analysis. Comput Method Appl Mech Eng 79(2):219–244. doi: 10.1016/0045-7825(90)90133-7
- 33.Hsiao GC, Wendland W (1991) Domain decomposition in boundary element method. Paper presented at the fourth international symposium on domain decomposition methods for partial differential equations, PhiladelphiaGoogle Scholar
- 44.Pechstein C (2009) Boundary element tearing and interconnecting methods in unbounded domains. Appl Numer Math 59(11):2824–2842. doi: 10.1016/j.apnum.2008.12.031