Weighted Radial Basis Collocation Method for the Nonlinear Inverse Helmholtz Problems
Abstract
:1. Introduction
2. Approximation of Radial Basis Functions
3. Formulations for the Inverse Helmholtz Problem of Identifying Parameter
3.1. Discretization of the Governing Equation as Well as Boundary Conditions and Known Conditions
3.2. Least-Squares Solution
4. Numerical Solutions of Some Representative Examples
4.1. One-Dimensional Inverse Helmholtz Problem of Constant Parameter Identification
4.2. Two-Dimensional Inverse Helmholtz Problem of Constant Parameter Identification in Irregular Geometry
4.3. Two-Dimensional Inverse Helmholtz Problem of Parameter Identification
4.4. Three-Dimensional Inverse Helmholtz Problem of Parameter Identification in Cubic Domain
4.5. Three-Dimensional Inverse Helmholtz Problem of Parameter Identification in Spherical Domain
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Hu, M.; Wang, L.; Yang, F.; Zhou, Y. Weighted Radial Basis Collocation Method for the Nonlinear Inverse Helmholtz Problems. Mathematics 2023, 11, 662. https://doi.org/10.3390/math11030662
Hu M, Wang L, Yang F, Zhou Y. Weighted Radial Basis Collocation Method for the Nonlinear Inverse Helmholtz Problems. Mathematics. 2023; 11(3):662. https://doi.org/10.3390/math11030662
Chicago/Turabian StyleHu, Minghao, Lihua Wang, Fan Yang, and Yueting Zhou. 2023. "Weighted Radial Basis Collocation Method for the Nonlinear Inverse Helmholtz Problems" Mathematics 11, no. 3: 662. https://doi.org/10.3390/math11030662
APA StyleHu, M., Wang, L., Yang, F., & Zhou, Y. (2023). Weighted Radial Basis Collocation Method for the Nonlinear Inverse Helmholtz Problems. Mathematics, 11(3), 662. https://doi.org/10.3390/math11030662