Results 1 to 10 of about 23,622 (294)
Boundary regularized integral equation formulation of the Helmholtz equation in acoustics [PDF]
Royal Society Open Science, 2015 A boundary integral formulation for the solution of the Helmholtz equation is developed in which all traditional singular behaviour in the boundary integrals is removed analytically.
Qiang Sun +3 more
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Generalized Helmholtz equation
Selecciones Matemáticas, 2019 In this paper we introduce the generalized Helmholtz equation and present explicit solutions to this generalized Helmholtz equation, these solutions depend on three holomorphic functions.
Carlos C. Riveros, Armando V. Corro
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Some properties and applications of the Teodorescu operator associated to the Helmholtz equation [PDF]
Journal of Inequalities and Applications, 2017 In this paper, we first define the Teodorescu operator T ψ , α $T_{\psi,\alpha }$ related to the Helmholtz equation and discuss its properties in quaternion analysis.
Pei Yang, Liping Wang, Long Gao
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Communications in Contemporary Mathematics, 2022 We show the equivalence of the classical Helmholtz equation and the fractional Helmholtz equation with arbitrary order. This improves a recent result of Guan, Murugan and Wei [Helmholtz solutions for the Fractional Laplacian and other related operators, to appear in Comm. Contemp. Math.].
Cheng, Xinyu, Li, Dong, Yang, Wen
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Is the Helmholtz Equation Really Sign-Indefinite? [PDF]
SIAM Review, 2014 The usual variational (or weak) formulations of the Helmholtz equation are sign-indefinite in the sense that the bilinear forms cannot be bounded below by a positive multiple of the appropriate norm squared. This is often for a good reason, since in bounded domains under certain boundary conditions the solution of the Helmholtz equation is not unique ...
Andrea Moiola, Euan A. Spence
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A robust approach for computing solutions of fractional-order two-dimensional Helmholtz equation [PDF]
Scientific ReportsThe Helmholtz equation plays a crucial role in the study of wave propagation, underwater acoustics, and the behavior of waves in the ocean environment. The Helmholtz equation is also used to describe propagation through ocean waves, such as sound waves ...
Muhammad Nadeem +3 more
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Helmholtz Resonance in Korean Bells
International Scholastic Journal of Science, 2017 Traditional Korean bells are installed above a shallow well with a gap between the bell and the ground, effectively creating a Helmholtz resonator. During installation, the size of the well and the gap is traditionally adjusted, through trial and error ...
Junghyun Kim
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Finite volume method for solving the stochastic Helmholtz equation
Advances in Difference Equations, 2019 In this paper, we consider the linear finite volume method (FVM) for the stochastic Helmholtz equation, driven by white noise perturbed forcing terms in one-dimension. We first deduce the linear FVM for the deterministic Helmholtz problem. The dispersion
Ruimin Xu, Tingting Wu
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On a fourth‐order nonlinear Helmholtz equation
Journal of the London Mathematical Society, 2018 In this paper, we study the mixed dispersion fourth order nonlinear Helmholtz equation $Δ^2 u -βΔu + αu= Γ|u|^{p-2} u$ in $\mathbb R^N$ for positive, bounded and $\mathbb Z^N$-periodic functions $Γ$. Using the dual method of Evequoz and Weth, we find solutions to this equation and establish some of their qualitative properties.
Denis Bonheure +2 more
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Solving eigenvalues problems for Helmholtz equation by point-source method
Advanced Engineering Research, 2016 A method of problem solution of the eigenvalues and eigenfunctions for the Helmholtz equation in the domains with arbitrary configuration is worked out.
Elena E. Shcherbakova
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