Simulations and analysis of underwater acoustic wave propagation model based on Helmholtz equation
In this study, we explore the effectiveness of elliptic partial differential equations (PDEs) in two and three dimensional space based on Helmholtz equation for simulations of acoustic sound in a very complex environment of propagation. For this purpose, we use an advance and robust numerical techni...
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2024-12-01
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| Series: | Applied Mathematics in Science and Engineering |
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| Online Access: | https://www.tandfonline.com/doi/10.1080/27690911.2024.2338397 |
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| author | Maryam Ahmed Alanazi Ishtiaq Ali |
| author_facet | Maryam Ahmed Alanazi Ishtiaq Ali |
| author_sort | Maryam Ahmed Alanazi |
| collection | DOAJ |
| description | In this study, we explore the effectiveness of elliptic partial differential equations (PDEs) in two and three dimensional space based on Helmholtz equation for simulations of acoustic sound in a very complex environment of propagation. For this purpose, we use an advance and robust numerical technique by utilizing the properties of shifted Chebyshev spectral collocation method. This technique is an extension of the traditional Chebyshev polynomials, incorporating a shift in their argument to enhance flexibility across a wider domain, while retaining an extraordinary numerical characteristic such as orthogonality and spectral convergence making them exceptionally effective in finding the approximate solutions. The exponential order of convergence of the proposed approach is shown both through theoretical and numerical approaches. We provide a number of numerical experiments to verify the theoretical results. The spectral convergence has been substantially enhanced by these numerical examples. The exponential order is further validated by numerical error behaviour in both [Formula: see text] and [Formula: see text] norms. |
| format | Article |
| id | doaj-art-30c92df6d0254ee3887b37056da811f8 |
| institution | Kabale University |
| issn | 2769-0911 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | Applied Mathematics in Science and Engineering |
| spelling | doaj-art-30c92df6d0254ee3887b37056da811f82024-12-06T04:24:25ZengTaylor & Francis GroupApplied Mathematics in Science and Engineering2769-09112024-12-0132110.1080/27690911.2024.2338397Simulations and analysis of underwater acoustic wave propagation model based on Helmholtz equationMaryam Ahmed Alanazi0Ishtiaq Ali1Department of Mathematics and Statistics, College of Science, King Faisal University, Al-Ahsa, Saudi ArabiaDepartment of Mathematics and Statistics, College of Science, King Faisal University, Al-Ahsa, Saudi ArabiaIn this study, we explore the effectiveness of elliptic partial differential equations (PDEs) in two and three dimensional space based on Helmholtz equation for simulations of acoustic sound in a very complex environment of propagation. For this purpose, we use an advance and robust numerical technique by utilizing the properties of shifted Chebyshev spectral collocation method. This technique is an extension of the traditional Chebyshev polynomials, incorporating a shift in their argument to enhance flexibility across a wider domain, while retaining an extraordinary numerical characteristic such as orthogonality and spectral convergence making them exceptionally effective in finding the approximate solutions. The exponential order of convergence of the proposed approach is shown both through theoretical and numerical approaches. We provide a number of numerical experiments to verify the theoretical results. The spectral convergence has been substantially enhanced by these numerical examples. The exponential order is further validated by numerical error behaviour in both [Formula: see text] and [Formula: see text] norms.https://www.tandfonline.com/doi/10.1080/27690911.2024.2338397Acoustic wave propagation modelHelmholtz equationshifted Chebyshev polynomialserror analysisnumerical simulations41A10 |
| spellingShingle | Maryam Ahmed Alanazi Ishtiaq Ali Simulations and analysis of underwater acoustic wave propagation model based on Helmholtz equation Applied Mathematics in Science and Engineering Acoustic wave propagation model Helmholtz equation shifted Chebyshev polynomials error analysis numerical simulations 41A10 |
| title | Simulations and analysis of underwater acoustic wave propagation model based on Helmholtz equation |
| title_full | Simulations and analysis of underwater acoustic wave propagation model based on Helmholtz equation |
| title_fullStr | Simulations and analysis of underwater acoustic wave propagation model based on Helmholtz equation |
| title_full_unstemmed | Simulations and analysis of underwater acoustic wave propagation model based on Helmholtz equation |
| title_short | Simulations and analysis of underwater acoustic wave propagation model based on Helmholtz equation |
| title_sort | simulations and analysis of underwater acoustic wave propagation model based on helmholtz equation |
| topic | Acoustic wave propagation model Helmholtz equation shifted Chebyshev polynomials error analysis numerical simulations 41A10 |
| url | https://www.tandfonline.com/doi/10.1080/27690911.2024.2338397 |
| work_keys_str_mv | AT maryamahmedalanazi simulationsandanalysisofunderwateracousticwavepropagationmodelbasedonhelmholtzequation AT ishtiaqali simulationsandanalysisofunderwateracousticwavepropagationmodelbasedonhelmholtzequation |