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Continuous charge distribution. The volume charge density ρ is the amount of charge per unit volume (cube), surface charge density σ is amount per unit surface area (circle) with outward unit normal nĚ‚, d is the dipole moment between two point charges, the volume density of these is the polarization density P.
Elements and operations of the algebra can generally be associated with geometric meaning. The members of the algebra may be decomposed by grade (as in the formalism of differential forms) and the (geometric) product of a vector with a k-vector decomposes into a (k − 1)-vector and a (k + 1)-vector.
Thomson JJ, Elements of the Mathematical Theory of Electricity and Magnetism, 4th ed, Cambridge University, 1909. Whittaker ET , A History of the Theories of Aether and Electricity , 2nd ed, 2 vols, Thomas Nelson , 1951.
The solutions are represented with the linear combination of pre-defined basis functions; generally, the coefficients of these basis functions are the sought unknowns. Green's functions and Galerkin method play a central role in the method of moments. For many applications, the method of moments is identical to the boundary element method.
The boundary element method (BEM) is a numerical computational method of solving linear partial differential equations which have been formulated as integral equations (i.e. in boundary integral form), including fluid mechanics, acoustics, electromagnetics (where the technique is known as method of moments or abbreviated as MoM), [1] fracture mechanics, [2] and contact mechanics.
Sinusoidal plane-wave solutions are particular solutions to the wave equation. The general solution of the electromagnetic wave equation in homogeneous, linear, time-independent media can be written as a linear superposition of plane-waves of different frequencies and polarizations .
Because of the linearity of Maxwell's equations in a vacuum, solutions can be decomposed into a superposition of sinusoids. This is the basis for the Fourier transform method for the solution of differential equations. The sinusoidal solution to the electromagnetic wave equation takes the form
FDFD simulation of light diffraction from a plasmonic slit. The finite-difference frequency-domain (FDFD) method is a numerical solution method for problems usually in electromagnetism and sometimes in acoustics, based on finite-difference approximations of the derivative operators in the differential equation being solved.