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Space-Time Multigrid Method for Space-Time Finite Element Discretizations of Parabolic and Hyperbolic PDEs

This repository contains the implementation of a space-time multigrid method based on tensor-product space-time finite element discretizations described in the paper "A Space-Time Multigrid Method for Space-Time Finite Element Discretizations of Parabolic and Hyperbolic PDEs" by Nils Margenberg and Peter Munch. The method leverages the matrix-free capabilities of the deal.II library and supports both high-order continuous and discontinuous variational time discretizations with spatial finite element discretizations. The implementation consistently performs well on perturbed meshes and can handle heterogeneous, discontinuous coefficients. We have demonstrated a throughput of over a billion degrees of freedom per second on problems with more than a trillion global degrees of freedom.

Usage

The code depends on a recent version of the deal.II library. We recommend using version 9.5.2 or a more recent one. To run the examples and replicate the results the scripts may need to be adapted to your system.

License

This project is licensed under the Apache License, Version 2.0 WITH LLVM-exception.

Authors

  • Nils Margenberg
  • Peter Munch

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