Title: Scalable solvers for complex electromagnetics problems,
Abstract: In this work, we present scalable balancing domain decomposition by
constraints methods for linear systems arising from arbitrary order edge finite
element discretizations of multi-material and heterogeneous 3D problems. In
order to enforce the continuity across subdomains of the method, we use a
partition of the interface objects (edges and faces) into sub-objects
determined by the variation of the physical coefficients of the problem. For
multi-material problems, a constant coefficient condition is enough to define
this sub-partition of the objects. For arbitrarily heterogeneous problems, a
relaxed version of the method is defined, where we only require that the
maximal contrast of the physical coefficient in each object is smaller than a
predefined threshold. Besides, the addition of perturbation terms to the
preconditioner is empirically shown to be effective in order to deal with the
case where the two coefficients of the model problem jump simultaneously across
the interface. The new method, in contrast to existing approaches for problems
in curl-conforming spaces, preserves the simplicity of the original
preconditioner, i.e., no spectral information is required, whilst providing
robustness with regard to coefficient jumps and heterogeneous materials. A
detailed set of numerical experiments, which includes the application of the
preconditioner to 3D realistic cases, shows excellent weak scalability
properties of the implementation of the proposed algorithms.