Results 31 to 40 of about 3,669,023 (333)
Helmholtz-Manakov solitons [PDF]
, 2005 A novel spatial soliton-bearing wave equation is introduced, the Helmholtz-Manakov (H-M) equation, for describing the evolution of broad multi-component self-trapped beams in Kerr-type media. By omitting the slowly-varying envelope approximation, the H-M
Chamorro-Posada, P +2 more
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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 +4 more
doaj +1 more source
Domain Decomposition preconditioning for high-frequency Helmholtz problems with absorption [PDF]
, 2016 In this paper we give new results on domain decomposition preconditioners for GMRES when computing piecewise-linear finite-element approximations of the Helmholtz equation $-\Delta u - (k^2+ {\rm i} \varepsilon)u = f$, with absorption parameter ...
Graham, Ivan G. +2 more
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Nonlinear interfaces: intrinsically nonparaxial regimes and effects [PDF]
, 2009 The behaviour of optical solitons at planar nonlinear boundaries is a problem rich in intrinsically nonparaxial regimes that cannot be fully addressed by theories based on the nonlinear Schrödinger equation.
Boardman A D +10 more
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Applied Mathematics Letters, 2019 Efficient evaluation of near-boundary and boundary solutions for the Helmholtz equation with wideband wavenumbers by the boundary collocation method has been a difficult task for a long time.
Junpu Li, Wen Chen, Zhuojia Fu, Q. Qin
semanticscholar +1 more source
A computing method for bending problem of thin plate on Pasternak foundation
Advances in Mechanical Engineering, 2020 The governing equation of the bending problem of simply supported thin plate on Pasternak foundation is degraded into two coupled lower order differential equations using the intermediate variable, which are a Helmholtz equation and a Laplace equation. A
Jiarong Gan +4 more
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Numerical solution of the two-dimensional Helmholtz equation with variable coefficients by the radial integration boundary integral and integro-differential equation methods [PDF]
, 2011 This is the author's accepted manuscript. The final published article is available from the link below. Copyright @ 2012 Taylor & Francis.This paper presents new formulations of the boundary–domain integral equation (BDIE) and the boundary–domain integro-
M. A. AL-Jawary +7 more
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Adaptive BEM with optimal convergence rates for the Helmholtz equation [PDF]
Computer Methods in Applied Mechanics and Engineering, 2018 We analyze an adaptive boundary element method for the weakly-singular and hypersingular integral equations for the 2D and 3D Helmholtz problem. The proposed adaptive algorithm is steered by a residual error estimator and does not rely on any a priori ...
A. Bespalov +3 more
semanticscholar +1 more source
A fast singular boundary method for 3D Helmholtz equation
Computers and Mathematics with Applications, 2019 This paper presents a fast singular boundary method (SBM) for three-dimensional (3D) Helmholtz equation. The SBM is a boundary-type meshless method which incorporates the advantages of the boundary element method (BEM) and the method of fundamental ...
Weiwei Li
semanticscholar +1 more source
Monotonicity and local uniqueness for the Helmholtz equation [PDF]
Analysis & PDE, 2017 This work extends monotonicity-based methods in inverse problems to the case of the Helmholtz (or stationary Schrodinger) equation $(\Delta + k^2 q) u = 0$ in a bounded domain for fixed non-resonance frequency $k>0$ and real-valued scattering coefficient
B. Harrach, V. Pohjola, M. Salo
semanticscholar +1 more source