KMS Of Academy of mathematics and systems sciences, CAS
| A convergent low-wavenumber, high-frequency homogenization of the wave equation in periodic media with a source term | |
Meng, Shixu1 ; Oudghiri-Idrissi, Othman2; Guzina, Bojan B.2
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| 2021-06-04 | |
| Source Publication | APPLICABLE ANALYSIS
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| ISSN | 0003-6811 |
| Pages | 34 |
| Abstract | We pursue a low-wave number, second-order homogenized solution of the time-harmonic wave equation at both low and high frequency in periodic media with a source term whose frequency resides inside a band gap. Considering the wave motion in an unbounded medium R-d (d >= 1), we first use the (Floquet-)Bloch transform to formulate an equivalent variational problem in a bounded domain. By investigating the source term's projection onto certain periodic functions, the second-order model can then be derived via asymptotic expansion of the Bloch eigenfunction and the germane dispersion relationship. We establish the convergence of the second-order homogenized solution, and we include numerical examples to illustrate the convergence result. |
| Keyword | Waves in periodic media dynamic homogenization finite frequency band gap (Floquet-)Bloch transform variational formulation |
| DOI | 10.1080/00036811.2021.1929932 |
| Indexed By | SCI |
| Language | 英语 |
| WOS Research Area | Mathematics |
| WOS Subject | Mathematics, Applied |
| WOS ID | WOS:000659433300001 |
| Publisher | TAYLOR & FRANCIS LTD |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/58774 |
| Collection | 应用数学研究所 |
| Corresponding Author | Meng, Shixu |
| Affiliation | 1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Appl Math, Beijing, Peoples R China 2.Univ Minnesota, Dept Civil Environm & Geoengn, Minneapolis, MN 55415 USA |
| Recommended Citation GB/T 7714 | Meng, Shixu,Oudghiri-Idrissi, Othman,Guzina, Bojan B.. A convergent low-wavenumber, high-frequency homogenization of the wave equation in periodic media with a source term[J]. APPLICABLE ANALYSIS,2021:34. |
| APA | Meng, Shixu,Oudghiri-Idrissi, Othman,&Guzina, Bojan B..(2021).A convergent low-wavenumber, high-frequency homogenization of the wave equation in periodic media with a source term.APPLICABLE ANALYSIS,34. |
| MLA | Meng, Shixu,et al."A convergent low-wavenumber, high-frequency homogenization of the wave equation in periodic media with a source term".APPLICABLE ANALYSIS (2021):34. |
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