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cortner / JuLIPMaterials.jl

Collection of Tools for Computational Materials Science
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LGF Options #12

Open cortner opened 6 years ago

cortner commented 6 years ago

Collecting different options how to implement LGFs.

cortner commented 6 years ago

If we just integrate over the BZ, then the expression we get is something like (if I'm not mistaken)

G(x) - G(0) = \int_BZ g(k) sin^2(k . x / 2). dk

This is analytic away from k = 0. so how about splitting it into two integrands

\int_BZ f_1(x; k) + f_2(x; k)

where f_1 is supported in a ball B_r(0). and f_2(x; k) is C^inf in BZ. Then we can integrate f_2 using a standard uniform grid (MP) an we can integrate f_1 by transforming it to spherical coordinates -> that should completely remove the singularity?

cortner commented 6 years ago

@jjbraun no rush at all, but if you manage to check whether your surface integral formulation could be made to work, can you put a brief summary here?

thudso commented 6 years ago

A quick remark:

how about splitting it into two integrands

is basically Dallas' approach to computing the LGF.