Sentence examples for divergence gradient from inspiring English sources

Discretization process of the mathematical model is greatly simplified by three differential operators that are defined to represent the expressions of divergence, gradient and average as their original forms, and thus, enable rapid prototyping of the numerical model.

Here compatible means that the method retains discrete analogs of several key properties of the divergence, gradient and curl operators: the divergence and gradient are anti-adjoints (the negative transpose) of each other, the curl is self-adjoint and annihilates the gradient operator, and the divergence annihilates the curl.

Optimizations were applied mainly to the calculation parts (kernels) such as divergence, gradient, and Laplacian operations.

For other useful formulas including divergence, gradient, and Laplacian in polar coordinates, see curvilinear coordinates.

'∇' and '∇' indicate divergence and gradient operations, respectively.

end{aligned}Here and in what follows (text {div}) and (nabla ) denote the usual divergence and gradient in (mathbb {R}^{2n+1}).

where ∘ denotes the Hadamard (element wise) product, diagonal positive definite matrices for thermal conductivity and volumetric heat capacity M k, M ρ c, discrete divergence and gradient operators S ˜, − S ˜ ⊤ on the dual grid, respectively.

Recently, one of the authors developed a systematic approach to obtain mimetic finite difference discretizations for divergence and gradient operators, which achieves the same order of accuracy on the boundary and inner grid points.

The invariant form on a Riemannian manifold with boundary ( M, g ) for an isotropic conductivity β is given by div g ( β ∇ g ) u = 0 (90)where div g (resp. ∇ g ) denotes divergence (resp. gradient) with respect to the Riemannian metric g.

Vector calculus: gradient, divergence and curl, Green's, divergence and Stokes' theorems.

The Laplace operator will be defined as the divergence of the gradient.