Improvement of Integration of Green's tensor

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Integration of Green's tensor (IGT) over the cubical dipole is known to
increase the accuracy of DDA, at least for some problems (Chaumet et al.
"Coupled dipole method for scatterers with large permittivity." Phys. Rev.
E 70, 036606 (2004)). However, such integration is rather computationally
intensive, and a careful compromise between the accuracy and the speed
should be sought for.

The idea is first to implement a robust (and not optimized) version of the
Green's tensor, probably based on the codes by Patric Chaumet and Adel
Rahmani. After that is tested, it may be used to benchmark IGT performance
for refractive indices not covered in the original paper. 

Second, the computation of integrals should be optimized to make it fast
(desirably, not slower than a few iterations of an iterative solver). One
of the ideas for that is to use more accurate methods for close dipoles and
less accurate for dipoles far from each other. It can be combined with
tabulation of integrals on a finite cubical grid. These ideas are very
similar to ones, on which SO formulation is based (issue 37), so should not
be hard to implement. 

Original issue reported on code.google.com by yurkin on 7 Sep 2009 at 5:48

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Original comment by yurkin on 18 Sep 2009 at 9:22

• Added labels: Component-Logic

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It is important to perform "proper" tests for this formulation. For instance,
Rayleigh sphere is not suitable, because the internal electric field is 
constant -
hence IGT (if done accurately enough) completely eliminates discretization 
errors.
Thus only surface errors are left, which can be small for certain refractive 
indices.
So a small errors for a Rayleigh sphere with extreme refractive index indicate a
correct implementation of IGT, but not that it will be as good for other shapes.

However, other Rayleigh particle with relatively small variation of the internal
electric field (say, a cube) may also show rather small errors, when IGT is 
used. But
I think these errors will still be significantly larger than for a sphere.

Original comment by yurkin on 30 Sep 2009 at 9:50

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First part is finished at r832. IGT was implemented based on code provided by 
P.C.
Chaumet and A. Rahmani. A distance limit for using integration can be set, and 
it
seems that 1-3 dipoles is enough for most accuracy gain. Such small limit do not
require a lot of computational time. So IGT is ready for production runs.

Original comment by yurkin on 4 Nov 2009 at 6:20

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Original comment by yurkin on 6 Nov 2009 at 9:44

• Changed title: Improvement of Integration of Green's tensor

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Second part should be implemented by the end of 2010.

Original comment by yurkin on 22 Mar 2010 at 6:22

• Added labels: Milestone-2010, Priority-High
• Removed labels: Priority-Medium

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Original comment by yurkin on 22 Mar 2010 at 6:24

• Added labels: Priority-Critical
• Removed labels: Priority-High

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This issue was closed by revision r982.

Original comment by yurkin on 30 Sep 2010 at 5:53

• Changed state: Fixed