lebedev_laikov

Lebedev–Laikov quadrature for numerical integration in spherical coordinates.

In this scheme, surface integrals over the sphere are approximated as:

∫ f(Ω) dΩ = ∫ f(θ, φ) sin(θ) dθ dφ ≈ 4 π ∑ₖ wₖ f(xₖ, yₖ, zₖ)

Note that the weights are normalized such that they sum to one.

Usage

Building library requires a C compiler (but not Fortran). It uses C source code (bundled) translated from Fortran, originally hosted on ccl.net.

Reference

V. I. Lebedev, and D. N. Laikov, “A quadrature formula for the sphere of the 131st algebraic order of accuracy,” Doklady Mathematics, 59 (3), 477-481 (1999). http://rad.chem.msu.ru/~laikov/ru/DAN_366_741.pdf

lib.rs:

Lebedev–Laikov quadrature

Approximates surface integrals over the sphere as:

∫ f(Ω) dΩ = ∫ f(θ, φ) sin(θ) dθ dφ ≈ 4 π ∑ₖ wₖ f(xₖ, yₖ, zₖ)

Note that the weights are normalized such that they sum to one.

Reference

V. I. Lebedev, and D. N. Laikov, “A quadrature formula for the sphere of the 131st algebraic order of accuracy,” Doklady Mathematics, 59 (3), 477-481 (1999). http://rad.chem.msu.ru/~laikov/ru/DAN_366_741.pdf