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In numerical analysis, Lebedev quadrature, … In numerical analysis, Lebedev quadrature, named after Vyacheslav Ivanovich Lebedev, is an approximation to the surface integral of a function over a three-dimensional sphere. The grid is constructed so to have octahedral rotation and inversion symmetry. The number and location of the grid points together with a corresponding set of integration weights are determined by enforcing the exact integration of polynomials (or equivalently, spherical harmonics) up to a given order, leading to a sequence of increasingly dense grids analogous to the one-dimensional Gauss-Legendre scheme. The Lebedev grid is often employed in the numerical evaluation of volume integrals in the spherical coordinate system, where it is combined with a one-dimensional integration scheme for the radial coordinate. Applications of the grid are found in fields such as computational chemistry and neutron transport.utational chemistry and neutron transport.
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, https://bitbucket.org/CasperBeentjes/quadratures-on-unit-sphere/src/master/ +
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In numerical analysis, Lebedev quadrature, … In numerical analysis, Lebedev quadrature, named after Vyacheslav Ivanovich Lebedev, is an approximation to the surface integral of a function over a three-dimensional sphere. The grid is constructed so to have octahedral rotation and inversion symmetry. The number and location of the grid points together with a corresponding set of integration weights are determined by enforcing the exact integration of polynomials (or equivalently, spherical harmonics) up to a given order, leading to a sequence of increasingly dense grids analogous to the one-dimensional Gauss-Legendre scheme.the one-dimensional Gauss-Legendre scheme.
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Lebedev quadrature
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