# volume integral

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## volume integral

[′väl·yəm ′int·ə·grəl]
(mathematics)
An integral of a function of several variables with respect to volume measure taken over a three-dimensional subset of the domain of the function.
References in periodicals archive ?
Compared with a surface integral equation (SIE) such as a PMCHWT equation [2], a volume integral equation (VIE) is more flexible, robust, and accurate [3]; therefore, VIE is usually preferred or even the only option for complex dielectric anisotropic objects.
Their topics include the composite scattering and Doppler spectra of a moving ship at a time-evolving sea surface, volume integral equation solvers for electromagnetic scattering by penetrable objects, analytical formulations of scattering by finite circular cylinder and thin dielectric circular disk, electromagnetic wave scattering in dense media: applications in the remote sensing of sea ice and vegetation, and target feature extraction with polarimetric radar.
Generalized Born / Volume integral (GB / VI) implicit solvent method implemented in MOE was used to identify binding affinities of the hits with PIM kinases [21].
67), and then from an integral psychology perspective, 'Their model is presented in the ground-breaking volume Integral Ecology ...
The energy-momentum components are found by the volume integral:
In cases where the SIE methods are not available, integral equations based on volume discretizations [15], i.e., volume integral equation methods (VIEs), are required.
The 21 papers of this year's iteration include discussions of coupled multi-domain boundary element method and finite element method for analyzing interaction between fluids and structures, simulating pattern formation in reaction-diffusion systems by the local integral equation method, green element method solutions to steady inverse contaminant transport problems, an alternative dynamic fundamental solution for plate bending including the shear deformation effect, the inverse scattering analysis of elastic half space by means of the fast volume integral equation method, and the least squares method as a refining technique in boundary element method analysis.
Under this condition, it is feasible to replace the volume integral in Equation (6) by discrete summation.
If we consider the formulas for dm and dq, given before the relation (12), then the mass and the charge can be expressed in terms of the volume integral of the density of mass and charge:
Here, we discuss the impact of both Fourier factorization methods on the efficiency and accuracy of the volume integral method, formulated in the (transverse) spectral domain.
Among the topics are a boundary element solution of thermal creeping flow in a nanometer single mixer, evaluating interface cracks, rotational symmetry applied to boundary element computation for nuclear fusion plasma, fundamental solutions for inverse obstacle acoustic scattering, the volume integral equation method for analyzing scattered waves in an elastic half space, and analyzing layered soil problems with an alternative multi-region boundary element method technique and a new infinite boundary element formulation.
If one assumes such a boundary, like those in stationary solutions of the non-linear equations, the included energy becomes the volume integral within this boundary

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