The Fast Radial Basis Functions Orthogonal Gradients (RBF-OGr) method for solving PDEs on arbitrary surfaces
Cecile Piret (Mathematical Sciences, Michigan Technological University)
The RBF-OGr method was introduced in [Piret, 2012] to discretize differential operators defined on arbitrary manifolds defined exclusively by a point cloud. The method was designed to take advantage of the meshfree character of RBFs, which offers the flexibility to represent complex geometries in any spatial dimension while providing a high order of accuracy. A large limitation of the original RBF-OGr method was its large computational complexity, which greatly restricted the size of the point cloud. In this talk, a fast version of the RBF-OGr method will be introduced. This latest algorithm makes use of the RBF-Finite Difference (RBF-FD) technique for building sparse differentiation matrices discretizing continuous differential operators such as the Laplace-Beltrami or the surface biharmonic operators.