We present a matrix-free approach for implementing ghost penalty stabilization in Cut Finite Element Methods (CutFEM). 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 method is implemented within the \texttt{deal.II} library.

翻译：本文提出了一种在切割有限元方法中实现鬼罚项稳定的无矩阵方法。通过利用鬼罚项算子的张量积结构，我们将其评估简化为使用预计算的一维矩阵进行一系列一维矩阵-向量乘积，避免了直接计算高阶导数。该方法在$d$维空间中对于$k$阶单元实现了$O(k^{d+1})$的复杂度，在保持精度的同时显著降低了实现难度。该算法已在\texttt{deal.II}库中实现。