Power iterative multiple reciprocity boundary element method for solving three-dimensional Helmholtz eigenvalue problems
| Autor: | Shusuke Nishiyama, Takeaki Enoto, Masafumi Itagaki, Satoshi Tomioka, Naoki Sahashi |
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| Rok vydání: | 1997 |
| Předmět: |
Helmholtz equation
Applied Mathematics Mathematical analysis General Engineering Computational Mathematics symbols.namesake Reciprocity (electromagnetism) Helmholtz free energy Fundamental solution symbols Method of fundamental solutions T-matrix method Boundary element method Analysis Bessel function Mathematics |
| Zdroj: | Engineering Analysis with Boundary Elements. 20:113-121 |
| ISSN: | 0955-7997 |
| DOI: | 10.1016/s0955-7997(97)00055-6 |
| Popis: | The multiple reciprocity boundary element method (MRBEM) has been employed to solve the three-dimensional Helmholtz equation, ▿ 2 gf + k 2 gf = 0. In the present technique, the Helmholtz equation is arranged as ▿ 2 gf + k 0 2 gf + gf / γ = 0 where k 0 is an estimate of k and λ is equal to ( k 2 − k 0 2 ) −1 . As the term gf/λ is treated as a source, the power iteration technique with Wielandt's spectral shift is used to find the value of λ. The boundary integral equation is formulated with the fundamental solution to ▿ 2 gf + k 0 2 gf + δ i = 0. The domain integral related to the above source is transformed into a series of boundary integrals, with the aid of the higher order fundamental solutions based on the spherical Bessel functions. The eigenvalue k 2 can also be described using only boundary integrals. Test calculations demonstrate that the present technique is efficient for finding k 2 and easier to handle than the conventional determinant search scheme. |
| Databáze: | OpenAIRE |
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