Matrix-free ghost penalty evaluation via tensor product factorization
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 address...
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| Autore principale: | |
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| Natura: | Article (Journal) |
| Lingua: | inglese |
| Pubblicazione: |
29 March 2026
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| In: |
Computers and mathematics with applications
Year: 2026, Volume: 211, Pages: 109-121 |
| ISSN: | 1873-7668 |
| DOI: | 10.1016/j.camwa.2026.03.013 |
| Accesso online: | Verlag, kostenfrei, Volltext: https://doi.org/10.1016/j.camwa.2026.03.013 Verlag, kostenfrei, Volltext: https://www.sciencedirect.com/science/article/pii/S089812212600115X 
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| Note sull'autore: | Michał Wichrowski |
| Riassunto: | 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(kd+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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| Descrizione del documento: | Gesehen am 28.05.2026 Online veröffentlicht: 29. März 2026 |
| Descrizione fisica: | Online Resource |
| ISSN: | 1873-7668 |
| DOI: | 10.1016/j.camwa.2026.03.013 |