
Efficient band structure computation of 3D photonic crystals
A parallel multigrid method with higher order modified finite elements for the 3D periodic eigenvalue problem in the curl-curl formulation
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The band structure computation turns into solving a family of Maxwell eigenvalue problems on the periodicity domain. The discretization is done by the finite element method with special higher order H(curl)- and H1-conforming modified elements. The eigenvalue problem is solved by a preconditioned iterative eigenvalue solver with a projection onto the divergence-free vector fields. As a preconditioner we use the parallel multigrid method with a special Hiptmair smoother.