A parallel space-time multigrid method for the eddy-current equation

Abstract

We expand the applicabilities and capabilities of an already existing space-time parallel method based on a block Jacobi smoother. First we formulate a more detailed criterion for spatial coarsening, which enables the method to deal with unstructured meshes and varying material parameters. Further we investigate the application to the eddy-current equation, where the non-trivial kernel of the curl operator causes severe problems. This is remedied with a new nodal auxiliary space correction. We proceed to identify convergence rates by local Fourier analysis and numerical experiments. Finally, we present a numerical experiment which demonstrates its excellent scaling properties.