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：提出了一个新的数字域分解方法,用于解决紧凑的里曼尼方形上的椭圆方程式。 这种方法的优点是避免在多元体上进行全球三角或网格。 我们的方法是用数字测试大约4美元的维数, 如单位球 $S ⁇ 4} 美元、 复杂的投影空间$mathbb{CP ⁇ 2} 美元和产品 $S ⁇ 2}\times S ⁇ 2} 美元。