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

TL;DR

This paper enhances a space-time parallel multigrid method to effectively solve the eddy-current equation on unstructured meshes with varying materials, introducing a new correction and demonstrating excellent scalability.

Contribution

It introduces a detailed spatial coarsening criterion, a nodal auxiliary space correction for curl operator issues, and validates the method's convergence and scalability.

Findings

Effective handling of unstructured meshes and material variations.

Successful correction of curl operator kernel issues.

Demonstrated excellent parallel scalability.

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.