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link > Peformance of iterative solvers in the discrete dipole approximation by Maxim A. Yurkin (2016) | grouping of iterative solvers | Estimate of N_iter | spectral radius

Last updated at Posted at 2017-09-29
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A presentation given at International Symposium on Electromagnetic Theory (EMTS 2016),Espoo, Finland, 17.08.2016.
https://www.researchgate.net/publication/307477398_Slides_EMTS-2016_iter

p8

asymptotic behavior of N_iter for large scatterers

p9

QMR, QMR2, Bi-CG complex symmetric
Bi-CGStab, Bi-CGStab(2) general CG-type method
CGNR, CSYM solve normalized equations

p26 Estimate of N_iter
for large sizes

N_{iter} \approx \frac{15 ln 10 \rho(Z)}{4 Im(1/(1-\epsilon))}

p28 Estimate of the spectral radius

\rho(Z) \approx 4.5 + 0.14 x

The graph is drawn for x ranging from 10 to 100.

link

number of iterationve becoms large for QMR for specific Re{m} and Im{m} (e.g., m=1.5 + 0.001i)

It gives several contour plots, similar to your ones, and provides a few analytical formula, but they are applicable only to either very small or very large particles. In your "resonant" case of particles comparable to the wavelength it is hard to predict anything, apart from the general trends - #ite inreases with size and refractive index, and almost real or imaginary refractive indices are the toughest.

ADDA + Matplotlib > scatterplot of [the number of iterations] for various values of Re{m} and Im{m}, for different iterative solvers (e.g., bicgstab2, bicg, QMR, etc)

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