A Scalable and Robust Vertex-Star Relaxation for High-Order FEM

@article{Brubeck2022ASA,
  title={A Scalable and Robust Vertex-Star Relaxation for High-Order FEM},
  author={Pablo D Brubeck and Patrick E. Farrell},
  journal={SIAM Journal on Scientific Computing},
  year={2022}
}
Pavarino proved that the additive Schwarz method with vertex patches and a loworder coarse space gives a p-robust solver for symmetric and coercive problems [33]. However, for very high polynomial degree it is not feasible to assemble or factorize the matrices for each patch. In this work we introduce a direct solver for separable patch problems that scales to very high polynomial degree on tensor product cells. The solver constructs a tensor product basis that diagonalizes the blocks in the… 

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