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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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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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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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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 Solving and Performance Optimization in Global/Regional Assimilation and Prediction System
Tsinghua Science and Technology, 2021 Despite efficient parallelism in the solution of physical parameterization in the Global/Regional Assimilation and Prediction System (GRAPES), the Helmholtz equation in the dynamic core, with the increase of resolution, can hardly achieve sufficient ...
Jianqiang Huang +5 more
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Mathematics, 2023 In this work, it is shown that the geometry of a gravity field generated by a spheroid with low eccentricity can be described with the help of a newly modified Helmholtz equation.
Gerassimos Manoussakis
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Solvability of discrete Helmholtz equations
IMA Journal of Numerical Analysis, 2022 Abstract We study the unique solvability of the discretized Helmholtz problem with Robin boundary conditions using a conforming Galerkin finite element method. Well-posedness of the discrete equations is typically investigated by applying a compact perturbation argument to the continuous Helmholtz problem so that a `sufficiently rich ...
Bernkopf, Maximilian +3 more
openaire +4 more sources
Journal of Mathematics, 2022 The Quasi-Reversibility Regularization Method (Q-RRM) provides stable approximate solution of the Cauchy problem of the Helmholtz equation in the Hilbert space by providing either additional information in the Laplace-type operator in the Helmholtz ...
Benedict Barnes +3 more
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An analytical method for shallow spherical shell free vibration on two-parameter foundation
Heliyon, 2021 The free vibration control differential equation of shallow spherical shell on two-parameter foundation is a four order differential equation.
Jiarong Gan +4 more
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