Helmholtz equation


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Helmholtz equation

[′helm‚hōlts i‚kwā·zhən]
(mathematics)
A partial differential equation obtained by setting the Laplacian of a function equal to the function multiplied by a negative constant.
(optics)
An equation which relates the linear and angular magnifications of a spherical refracting interface. Also known as Lagrange-Helmholtz equation.
(physical chemistry)
The relationship stating that the emf (electromotive force) of a reversible electrolytic cell equals the work equivalent of the chemical reaction when charge passes through the cell plus the product of the temperature and the derivative of the emf with respect to temperature.
References in periodicals archive ?
The 26 papers selected for publication consider such topics as a kind of Riemann boundary value problem for tri-harmonic functions in Clifford analysis, high-frequency asymptotics for the modified Helmholtz equation in a half-plane, positive solutions of singular third-order three-point boundary value problems, the numerical simulation of long-period ground motion on basin effects, and the second fundamental problem of periodic plane elasticity of a one-dimensional hexagonal quasicrystal.
6) Beam Propagation Method (BPM): A numerical analysis technique in electromagnetics for solving the Helmholtz equation under conditions of a time-harmonic wave.
The model was solved at first by using one of the most commonly employed algorithms for matrices arising from finite element formulations for the Helmholtz equation (Von Erstoff et al.
Finite element solution to the Helmholtz equation with high wave number Part I: The h-version of the FEM.
mu][epsilon](x) = 1, it is then clear that one is led to deal with the Helmholtz equation.
Helmholtz equation, for which a complete set of boundary conditions are not available.
Many applications in physics deal with the Helmholtz equation in three dimensions.
j] is a solution of the vector Helmholtz equation [[DELTA].
The idea of linking gravitation with wave mechanics of Quantum Mechanics reminds us to the formal connection between Helmholtz equation and Schrodinger equation [22].
12] --, Sine inversion of the Helmholtz equation without computing the forward solution, in Proc.
In static conditions (11) coincides with the Helmholtz equation.
The numerical solution of sequences of algebraic linear systems from the discretization of the real and complex Helmholtz equation and of the diffusion equation in a rectangle illustrate the performance of the proposed approaches.