2013 Fiscal Year Final Research Report
Development and application of the fast algorithm for the time-domain boundary element method for transient wave problems
| Project/Area Number |
24656072
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Single-year Grants |
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| Research Field |
Engineering fundamentals
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| Research Institution | Nagoya University |
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Principal Investigator |
TAKAHASHI Toru 名古屋大学, 工学(系)研究科(研究院), 講師 (90360578)
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| Project Period (FY) |
2012-04-01 – 2014-03-31
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| Keywords | 境界要素法 / 高速多重極法 / 波動方程式 / 関数補間 / 反復解法 / 音響問題 / 高速解法 / 非定常問題 |
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| Research Abstract |
The bottleneck of the boundary element method is its high computational cost, although the method is very accurate for the transient wave problems. To overcome this difficulty, the present study proposed an FMM-like fast algorithm and developed a fast boundary element method for wave problems in time domain. Specifically, the idea to approximate a two-body interaction function with polynomials in order to obtain its representation in the separation of variables, which originates from the black-box fast multiple method, is applied to the time-dependent Green's function for the three-dimensional scalar wave equation of interest. As a result, a time-domain interpolation-based fast multipole method was developed successfully. Through the numerical experiments with the implemented computer program, the proposed method was validated.
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