DomainDecompositionΒΆ
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This is the only available preconditioner in JCMsuite for time-harmonic wave scattering problems. For this type of problems an algebraic direct solver (see Direct) typically outperforms an iterative scheme with respect to computation time. An iterative solver hardly reproduces multiple scattering phenomena especially in the presence of resonance modes.
However a direct solver is heavily restricted by its memory demands. Therefore the reduction of memory usage is the main focus of the domain decomposition method. This is achieved by splitting the entire problem into smaller sub-domain problems. Each sub-domain is surrounded by a shell layer overlapping into neighbouring sub-domain, see ShellRadius. Within the shelling region an artificial damping of the wave propagation is applied to mitigate spurious reflections from the interfaces introduced by the splitting. On each sub-problem (sub-domain together with the overerlapping shell region) a direct solver is applied.
As a best practice advice you may follow the following guideline:
- Use direct solvers as long as your problem fits into your computer resources. In case of memory shortage switch to an iterative scheme together in combination with the domain decomposition preconditioner.
- Try to maximize the sub-domain volume to benefit from the direct solver as much as possible.
- In case of a weak convergence rate it may help to increase the shell layer or to apply more artificial damping.
- When limiting the number of iterations of the outer solver (MaxIterations) the computed approximation may already provides satisfactory results for your post-process quantities such as far field coefficients.
- The convergence rate my differ even between similar problems depending on how much resonance effects matter.
The two last two points are related to the multi-scale nature of wave propagation. A coherent coupling between far distant features of your optical device may lead to a slow convergence rate. But for your specific application a physcial reasonable approximation might reproduce your quantity of interest sufficiently. For example a long-range coherent coupling could become irrelevant due a limited coherence length of the optical source field. Or it might not be relevant to distinguish for example between trapped light and stray light or other loss mechanism. So often one observes a cascade of the convergence rate in the iterative solution process. Local coupling effects in the range of the sub-domain diameters are quickly resolved. Improving the solution further requires more iterations to capture the long-distance coherence effects which leads to a degradation of the convergene rate.