Results 1 to 10 of about 3,283,376 (328)

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
doaj   +5 more sources

On a fourth order nonlinear Helmholtz equation [PDF]

Journal of the London Mathematical Society, 2018
In this paper, we study the mixed dispersion fourth order nonlinear Helmholtz equation $\Delta^2 u -\beta \Delta u + \alpha u= \Gamma|u|^{p-2} u$ in $\mathbb R^N$ for positive, bounded and $\mathbb Z^N$-periodic functions $\Gamma$.
Abramowitz M., Bonheure D., Bonheure D., Denis Bonheure, Evéquoz G., Gilbarg D., Jean‐Baptiste Casteras, Lorenzi L., Rainer Mandel, Stein E. M., Stein E. M., Sulem C.   +11 more
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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

The Extrinsic Enriched Finite Element Method with Appropriate Enrichment Functions for the Helmholtz Equation

Mathematics, 2023
The traditional finite element method (FEM) could only provide acceptable numerical solutions for the Helmholtz equation in the relatively small wave number range due to numerical dispersion errors.
Yingbin Chai, Kangye Huang, Shangpan Wang, Zhichao Xiang, Guanjun Zhang   +4 more
doaj   +2 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

Sharp high-frequency estimates for the Helmholtz equation and applications to boundary integral equations [PDF]

SIAM Journal on Mathematical Analysis, 2015
We consider three problems for the Helmholtz equation in interior and exterior domains in R^d (d=2,3): the exterior Dirichlet-to-Neumann and Neumann-to-Dirichlet problems for outgoing solutions, and the interior impedance problem.
Baskin, Dean, Spence, Euan, Wunsch, Jared   +2 more
core   +5 more sources

Additive Sweeping Preconditioner for the Helmholtz Equation [PDF]

Multiscale Modeling & simulation, 2016
We introduce a new additive sweeping preconditioner for the Helmholtz equation based on the perfect matched layer (PML). This method divides the domain of interest into thin layers and proposes a new transmission condition between the subdomains where ...
Liu, Fei, Ying, Lexing
core   +3 more sources

Modified Finite Difference Schemes on Uniform Grids for Simulations of the Helmholtz Equation at Any Wave Number

Journal of Applied Mathematics, 2014
We construct modified forward, backward, and central finite difference schemes, specifically for the Helmholtz equation, by using the Bloch wave property.
Hafiz Abdul Wajid
exaly   +2 more sources

Multigrid-augmented deep learning preconditioners for the Helmholtz equation [PDF]

SIAM Journal on Scientific Computing, 2022
In this paper, we present a data-driven approach to iteratively solve the discrete heterogeneous Helmholtz equation at high wavenumbers. In our approach, we combine classical iterative solvers with convolutional neural networks (CNNs) to form a ...
Yael Azulay, Eran Treister
semanticscholar   +1 more source