Matrix-Free Ghost Penalty Evaluation via Tensor Product Factorization

2025/02/28 by Wichrowski, Michał · 1 citation
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2503.00246

Abstract

We present a matrix-free approach for implementing ghost penalty stabilization in Cut Finite Element Methods (CutFEM). While matrix-free methods for CutFEM have been developed, the efficient evaluation of high-order, face-based ghost penalties remains a significant challenge, which this work addresses. By exploiting the tensor-product structure of the ghost penalty operator, we reduce its evaluation to a series of one-dimensional matrix-vector products using precomputed 1D matrices, avoiding the need to evaluate high-order derivatives directly. This approach achieves O(k^d+1) complexity for elements of degree k in d dimensions, significantly reducing implementation effort while maintaining accuracy. The derivation relies on the fact that the cells are aligned with the coordinate axes. The method is implemented within the deal.II library.

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