An efficient method for 3D Helmholtz equation with complex solution

M. H. Heydari; M. Hosseininia; D. Baleanu; M. H. Heydari; M. Hosseininia; D. Baleanu

doi:10.3934/math.2023756

AIMS Mathematics

2023, Volume 8, Issue 6: 14792-14819. doi: 10.3934/math.2023756

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Research article

An efficient method for 3D Helmholtz equation with complex solution

1.
Department of Mathematics, Shiraz University of Technology, Shiraz, Iran
2.
Department of Mathematics, Cankaya University, Ankara, Turkey
3.
Institute of Space Sciences, Magurele-Bucharest, R76900, Romania
4.
Lebanese American University, Beirut, Lebanon

Received: 17 February 2023 Revised: 07 April 2023 Accepted: 12 April 2023 Published: 21 April 2023
MSC : 32W50, 65M70

The Helmholtz equation as an elliptic partial differential equation possesses many applications in the time-harmonic wave propagation phenomena, such as the acoustic cavity and radiation wave. In this paper, we establish a numerical method based on the orthonormal shifted discrete Chebyshev polynomials for finding complex solution of this equation. The presented method transforms the Helmholtz equation into an algebraic system of equations that can be easily solved. Four practical examples are examined to show the accuracy of the proposed technique.
- 3D Helmholtz equation,
- orthonormal shifted discrete Chebyshev polynomials,
- complex solution
Citation: M. H. Heydari, M. Hosseininia, D. Baleanu. An efficient method for 3D Helmholtz equation with complex solution[J]. AIMS Mathematics, 2023, 8(6): 14792-14819. doi: 10.3934/math.2023756

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Abstract

The Helmholtz equation as an elliptic partial differential equation possesses many applications in the time-harmonic wave propagation phenomena, such as the acoustic cavity and radiation wave. In this paper, we establish a numerical method based on the orthonormal shifted discrete Chebyshev polynomials for finding complex solution of this equation. The presented method transforms the Helmholtz equation into an algebraic system of equations that can be easily solved. Four practical examples are examined to show the accuracy of the proposed technique.

References

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