Generalized finite difference method on unknown manifolds
Generalized finite difference method on unknown manifolds is a scholarly work, published in 2024 in ''Journal of Computational Physics''. The main subjects of the publication include mathematical analysis, finite difference, tangent, physics-informed neural networks, boundary, uncertainty quantification, applied mathematics, mathematics, boundary value problem, and tangent space. The authors establish the theoretical convergence of GFDM in solving Poisson PDEs and numerically demonstrate the accuracy on simple smooth manifolds of low and moderate high co-dimensions as well as unknown 2D surfaces.