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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, Evert Klaseboer, Boo-Cheong Khoo, Derek Y. C. Chan   +3 more
doaj   +4 more sources

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
doaj   +2 more sources

A robust approach for computing solutions of fractional-order two-dimensional Helmholtz equation [PDF]

Scientific Reports
The 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, Zitian Li, Devendra Kumar, Yahya Alsayaad   +3 more
doaj   +2 more sources

On the solution of the Helmholtz equation on regions with corners [PDF]

Proceedings of the National Academy of Sciences of the United States of America, 2016
Vladimir Rokhlin
exaly   +2 more sources

A New Modified Helmholtz Equation for the Expression of the Gravity Gradient and the Intensity of an Electrostatic Field in Spherical Harmonics

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
doaj   +1 more source

Solving the Helmholtz Equation Together with the Cauchy Boundary Conditions by a Modified Quasi-Reversibility Regularization Method

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, Isaac Addai, Francis Ohene Boateng, Ishmael Takyi   +3 more
doaj   +1 more source

Continuous operator method application for direct and inverse scattering problems

Журнал Средневолжского математического общества, 2021
We describe the continuous operator method for solution nonlinear operator equations and discuss its application for investigating direct and inverse scattering problems.
Boykov Ilya V., Roudnev Vladimir A., Boykova Alla I., Stepanov Nikita S.   +3 more
doaj   +1 more source

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, Hong Yuan, Shanqing Li, Qifeng Peng, Huanliang Zhang   +4 more
doaj   +1 more source

Solution to the Modified Helmholtz Equation for Arbitrary Periodic Charge Densities

Frontiers in Physics, 2021
We present a general method for solving the modified Helmholtz equation without shape approximation for an arbitrary periodic charge distribution, whose solution is known as the Yukawa potential or the screened Coulomb potential.
Miriam Winkelmann, Miriam Winkelmann, Miriam Winkelmann, Miriam Winkelmann, Miriam Winkelmann, Edoardo Di Napoli, Edoardo Di Napoli, Edoardo Di Napoli, Daniel Wortmann, Daniel Wortmann, Daniel Wortmann, Stefan Blügel, Stefan Blügel, Stefan Blügel   +13 more
doaj   +1 more source

PENENTUAN JENIS FUNGSI BASIS RADIAL DALAM DUAL RECIPROCITY BOUNDARY ELEMENT METHOD

Majalah Ilmiah Matematika dan Statistika, 2021
Problems involving modified Helmholtz equation are considered in this paper. To solve the problem numerically, dual reciprocity boundary element method (DRBEM) is employed.
Millatuz Zahroh
doaj   +1 more source