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math.NA2022★ 8 cited
Spectral methods for solving elliptic PDEs on unknown manifolds
Qile Yan, Shixiao Jiang, John Harlim
In this paper, we propose a mesh-free numerical method for solving elliptic PDEs on unknown manifolds, identified with randomly sampled point cloud data. The PDE solver is formulat…
math.NA2022★ 4 cited
Radial basis approximation of tensor fields on manifolds: From operator estimation to manifold learning
John Harlim, Shixiao Willing Jiang, John Wilson Peoples
In this paper, we study the Radial Basis Function (RBF) approximation to differential operators on smooth tensor fields defined on closed Riemannian submanifolds of Euclidean space…