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The Kirchhoff–Helmholtz integral combines the Helmholtz equation with the Kirchhoff integral theorem [1] to produce a method applicable to acoustics, [2] seismology ...
Kirchhoff's integral theorem (sometimes referred to as the Fresnel–Kirchhoff integral theorem) [1] is a surface integral to obtain the value of the solution of the homogeneous scalar wave equation at an arbitrary point P in terms of the values of the solution and the solution's first-order derivative at all points on an arbitrary closed surface (on which the integration is performed) that ...
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.
Kirchhoff's integral theorem, sometimes referred to as the Fresnel–Kirchhoff integral theorem, [3] uses Green's second identity to derive the solution of the homogeneous scalar wave equation at an arbitrary spatial position P in terms of the solution of the wave equation and its first order derivative at all points on an arbitrary closed surface as the boundary of some volume including P.
Its mathematical basis is the Kirchhoff–Helmholtz integral. It states that the sound pressure is completely determined within a volume free of sources, if sound pressure and velocity are determined in all points on its surface.
The analog of the 4D light field for sound is the sound field or wave field, as in wave field synthesis, and the corresponding parametrization is the Kirchhoff–Helmholtz integral, which states that, in the absence of obstacles, a sound field over time is given by the pressure on a plane. Thus this is two dimensions of information at any point ...
For example, a child who has a profound deficiency in growth hormone (especially if they are a cancer survivor with damage to the pituitary gland) may need to continue taking HGH as an adult, ...
The Helmholtz equation has a variety of applications in physics and other sciences, including the wave equation, the diffusion equation, and the Schrödinger equation for a free particle. In optics, the Helmholtz equation is the wave equation for the electric field. [1] The equation is named after Hermann von Helmholtz, who studied it in 1860. [2]