We propose and analyze a robust BPX preconditioner for the integral fractional Laplacian on bounded domains. For either quasi-uniform grids or graded bisection grids, we show that the condition numbers of the resulting systems remain uniformly bounded with respect to both the number of levels and the fractional power.

翻译：我们提议并分析一个强大的 BPX 在连接域块分数拉拉帕西安的必备条件。 对于准统一网格或分解分数网格,我们显示,由此形成的系统的条件数在水平数和分数功率方面仍然一致地受约束。