Before revision:  The method is applicable to div/curl-free vector fields in \mathbb{R \R ^2 and tangential fields on two-dimensional surfaces, such as the sphere, and the curl-free method can be generalized to vector fields in \mathbb{R \R ^d.
After revision:  The method is applicable to div/curl-free vector fields in \mathbb{R \R ^2 and tangential fields on two-dimensional surfaces, such as the sphere, and the curl-free method can be generalized to vector fields in \R ^d.