Results 271 to 280 of about 3,283,376 (328)
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2010
The Helmholtz equation $$(\Delta + k^2)w(x) = 0$$ (7.1) arises naturally in physical applications related to wave propagation and vibration phenomena. We mention several important examples.
Goong Chen, Goong Chen, Jianxin Zhou
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The Helmholtz equation $$(\Delta + k^2)w(x) = 0$$ (7.1) arises naturally in physical applications related to wave propagation and vibration phenomena. We mention several important examples.
Goong Chen, Goong Chen, Jianxin Zhou
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Layer Stripping for the Helmholtz Equation
SIAM Journal on Applied Mathematics, 1996Summary: We develop a new layer stripping technique for the inverse scattering problem for the one-dimensional Helmholtz equation on the half line. The technique eliminates the use of ``trace formulas'', relying instead on a nonlinear Plancherel equality that provides a simple and precise characterization of the reflection data.
Sylvester, John +2 more
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2001
The acoustic wave equation described the propagation of the sound in a medium like the air. It results, e.g., from the equation of the compressible gas dynamic, also called the compressible Navier-Stokes equations. In the case of small displacements of the gas, a linearization of these equations leads to an equation for the displacement and the small ...
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The acoustic wave equation described the propagation of the sound in a medium like the air. It results, e.g., from the equation of the compressible gas dynamic, also called the compressible Navier-Stokes equations. In the case of small displacements of the gas, a linearization of these equations leads to an equation for the displacement and the small ...
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1961
The vector Helmholtz equation, which occurs particularly in electromagnetic theory [19], is more complicated than the scalar Helmholtz equation and its separation presents new problems.
Parry Moon, Domina Eberle Spencer
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The vector Helmholtz equation, which occurs particularly in electromagnetic theory [19], is more complicated than the scalar Helmholtz equation and its separation presents new problems.
Parry Moon, Domina Eberle Spencer
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Journal of Mathematical Physics, 1978
In this paper, we introduce the spinor Helmholtz equation, a first order partial differential system, which, on the one hand, describes the behavior of a polarized electromagnetic beam at the Fresnel approximation and which, on the other hand, can also be used, from a numerical viewpoint, instead of the scalar Helmholtz equation for solving the ...
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In this paper, we introduce the spinor Helmholtz equation, a first order partial differential system, which, on the one hand, describes the behavior of a polarized electromagnetic beam at the Fresnel approximation and which, on the other hand, can also be used, from a numerical viewpoint, instead of the scalar Helmholtz equation for solving the ...
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Mean Value Integral Equations and the Helmholtz Equation
Results in Mathematics, 1996The author determines, with aid of spectral synthesis, all continuous functions which assume at each point of the real line or plane the integral mean of its values on a symmetric interval or circular disk of fixed radius, respectively. In the one dimensional case the solutions are exactly the examples found by \textit{W. Walter} [Result. Math. 26, No.
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Screen Problem for Vector Helmholtz Equation
Mathematische Nachrichten, 1999AbstractThe paper deals with the screen boundary value problem for vector Helmholtz equation in the three‐dimensional space. Using the method of boundary integral equations and the theory of elliptic pseudodifferential operators on manifolds with boundary we prove uniqueness and existence theorems in Bessel‐potential and Besov spaces and establish Cα ...
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Boundary Integral Equations for the Three-Dimensional Helmholtz Equation
SIAM Review, 1974The relation between various boundary integral equation formulations of Dirichlet and Neumann problems for the three-dimensional Helmholtz equation is clarified. The integral equations derived using single or double layer distributions as well as those based on the Helmholtz representation using an unmodified free space Green’s function are presented ...
Kleinman, R. E., Roach, G. F.
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, 2016
In this paper we present an overview of recent progress on the development and analysis of domain decomposition preconditioners for discretised Helmholtz problems, where the preconditioner is constructed from the corresponding problem with added ...
I. Graham, E. Spence, E. Vainikko
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In this paper we present an overview of recent progress on the development and analysis of domain decomposition preconditioners for discretised Helmholtz problems, where the preconditioner is constructed from the corresponding problem with added ...
I. Graham, E. Spence, E. Vainikko
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Symmetry Problems for the Helmholtz Equation
Applied Mathematics Letters, 2019Abstract Let D be a bounded domain in R 2 with a smooth boundary S , N be the unit normal to S pointing out of D , k > 0 is a constant. The class of over-determined problems of the type: ∇ 2 u + k 2 u = c 0 i n D , u | S = c 1 , u N
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