Solution of Helmholtz eigenvalue problems with non-regular domains using the direct interpolation technique
This work aims to evaluate the performance of the Direct Interpolation Boundary Element Method solving Helmholtz problems that present no regular geometric shapes. Using the radial basis functions, the Direct Interpolation Method approximates the non-self-adjoint kernel of the domain integral equati...
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| Format: | Article |
| Language: | English |
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Elsevier
2025-06-01
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| Series: | Partial Differential Equations in Applied Mathematics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666818125001627 |
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| author | Carlos Friedrich Loeffler Luciano de Oliveira Castro Lara Hercules de Melo Barcelos João Paulo Barbosa |
| author_facet | Carlos Friedrich Loeffler Luciano de Oliveira Castro Lara Hercules de Melo Barcelos João Paulo Barbosa |
| author_sort | Carlos Friedrich Loeffler |
| collection | DOAJ |
| description | This work aims to evaluate the performance of the Direct Interpolation Boundary Element Method solving Helmholtz problems that present no regular geometric shapes. Using the radial basis functions, the Direct Interpolation Method approximates the non-self-adjoint kernel of the domain integral equations, which appear in many partial differential equations of mathematics, physics, and engineering. Modeling the Helmholtz Equation, the Direct Interpolation Method approximates the inertia term by a sequence of radial basis functions. The technique has been used successfully in Poisson, Diffusive-advective, and Helmholtz problems, considering regular geometries and taking analytical solutions as a reference for performance evaluation. This paper evaluates the effects of the slenderness of the domain and the introduction of cuts on the boundary regarding the accuracy. Reference solutions are generated through Finite Element Method simulations using fine meshes. |
| format | Article |
| id | doaj-art-66a668b518c94d3a8ac62b10a8dc64c4 |
| institution | OA Journals |
| issn | 2666-8181 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Partial Differential Equations in Applied Mathematics |
| spelling | doaj-art-66a668b518c94d3a8ac62b10a8dc64c42025-08-20T02:02:19ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812025-06-011410123510.1016/j.padiff.2025.101235Solution of Helmholtz eigenvalue problems with non-regular domains using the direct interpolation techniqueCarlos Friedrich Loeffler0Luciano de Oliveira Castro Lara1Hercules de Melo Barcelos2João Paulo Barbosa3Mechanical Engineering Post-Graduate Program, Federal University of Espírito Santo, UFES, CT, Av. Fernando Ferrari, 540-Bairro Goiabeiras, 29075-910, Vitória, ES, BrazilMechanical Engineering Post-Graduate Program, Federal University of Espírito Santo, UFES, CT, Av. Fernando Ferrari, 540-Bairro Goiabeiras, 29075-910, Vitória, ES, BrazilNational Institute of Metrology, Quality, and Technology, INMETRO, CEP 25250-020, Duque de Caxias, RJ, Brazil; Corresponding author.Federal Institute of Espírito Santo, IFES, Campus São Mateus, Rodovia BR 101 Norte, Km 58 Litorâneo, 29932540, São Mateus, ES, BrazilThis work aims to evaluate the performance of the Direct Interpolation Boundary Element Method solving Helmholtz problems that present no regular geometric shapes. Using the radial basis functions, the Direct Interpolation Method approximates the non-self-adjoint kernel of the domain integral equations, which appear in many partial differential equations of mathematics, physics, and engineering. Modeling the Helmholtz Equation, the Direct Interpolation Method approximates the inertia term by a sequence of radial basis functions. The technique has been used successfully in Poisson, Diffusive-advective, and Helmholtz problems, considering regular geometries and taking analytical solutions as a reference for performance evaluation. This paper evaluates the effects of the slenderness of the domain and the introduction of cuts on the boundary regarding the accuracy. Reference solutions are generated through Finite Element Method simulations using fine meshes.http://www.sciencedirect.com/science/article/pii/S2666818125001627Boundary elements methodHelmholtz’s equationEigenvalues problemsIrregular geometric conformation |
| spellingShingle | Carlos Friedrich Loeffler Luciano de Oliveira Castro Lara Hercules de Melo Barcelos João Paulo Barbosa Solution of Helmholtz eigenvalue problems with non-regular domains using the direct interpolation technique Partial Differential Equations in Applied Mathematics Boundary elements method Helmholtz’s equation Eigenvalues problems Irregular geometric conformation |
| title | Solution of Helmholtz eigenvalue problems with non-regular domains using the direct interpolation technique |
| title_full | Solution of Helmholtz eigenvalue problems with non-regular domains using the direct interpolation technique |
| title_fullStr | Solution of Helmholtz eigenvalue problems with non-regular domains using the direct interpolation technique |
| title_full_unstemmed | Solution of Helmholtz eigenvalue problems with non-regular domains using the direct interpolation technique |
| title_short | Solution of Helmholtz eigenvalue problems with non-regular domains using the direct interpolation technique |
| title_sort | solution of helmholtz eigenvalue problems with non regular domains using the direct interpolation technique |
| topic | Boundary elements method Helmholtz’s equation Eigenvalues problems Irregular geometric conformation |
| url | http://www.sciencedirect.com/science/article/pii/S2666818125001627 |
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