A new numerical domain decomposition method is proposed for solving elliptic equations on compact Riemannian manifolds. The advantage of this method is to avoid global triangulations or grids on manifolds. Our method is numerically tested on some $4$-dimensional manifolds such as the unit sphere $S^{4}$, the complex projective space $\mathbb{CP}^{2}$ and the product manifold $S^{2} \times S^{2}$.

翻译：提出了一种新的数值区域分解法，用于求解紧致黎曼流形上的椭圆方程。该方法的优势在于避免了对流形进行全局三角剖分或网格划分。我们通过若干四维流形（例如单位球面 $S^{4}$、复射影空间 $\mathbb{CP}^{2}$ 以及乘积流形 $S^{2} \times S^{2}$）对该方法进行了数值测试。