Lebedev quadrature: Difference between revisions
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The '''Lebedev grid''' or '''Lebedev angular mesh''' is a set of [[grid point]]s on the [[unit sphere]], and their corresponding weights, usually used for [[numerical integration]] of [[numerical function]]s. defined on the angular [[spherical coordinates]], (<math>\theta</math> and <math>\phi</math>). |
The '''Lebedev grid''' or '''Lebedev angular mesh''' is a set of [[grid point]]s on the [[unit sphere]], and their corresponding weights, usually used for [[numerical integration]] of [[numerical function]]s. defined on the angular [[spherical coordinates]], (<math>\theta</math> and <math>\phi</math>). |
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Revision as of 02:28, 16 March 2008
The Lebedev grid or Lebedev angular mesh is a set of grid points on the unit sphere, and their corresponding weights, usually used for numerical integration of numerical functions. defined on the angular spherical coordinates, ( and ).
These grids have octahedral symmetry, and are defined such that spherical harmonic functions can be integrated exactly, up to a certain threshold. In practice, this means that highly accurate numerical integrations can be performed with fewer grid points.
Their main drawbacks are that they are not defined to arbitrary accuracy, and the and integrals are not performed separately. In other cases, numerical integration can be performed over a Gauss-Legendre angular mesh instead.