We propose a new numerical domain decomposition method for solving elliptic equations on compact Riemannian manifolds. One advantage of this method is its ability to bypass the need for global triangulations or grids on the manifolds. Additionally, it features a highly parallel iterative scheme. To verify its efficacy, we conduct numerical experiments on some $4$-dimensional manifolds without and with boundary.

翻译：我们提出了一种新的数值区域分解方法，用于求解紧致黎曼流形上的椭圆型方程。该方法的一个优势在于能够绕过对流形进行全局三角剖分或网格划分的需求。此外，它还具有高度并行的迭代格式。为验证其有效性，我们在某些无边界和带边界的四维流形上进行了数值实验。