The orthogonal gradients method: A radial basis functions method for solving partial differential equations on arbitrary surfaces

The orthogonal gradients method: A radial basis functions method for solving partial differential equations on arbitrary surfaces

Thu, 03/05/2012
14:00 		Dr Cécile Piret (Université catholique de Louvain.) Computational Mathematics and Applications Add to calendar Gibson Grd floor SR
The orthogonal gradients method: A radial basis functions method for solving partial differential equations on arbitrary surfaces
Although much work has been done on using RBFs for reconstructing arbitrary surfaces, using RBFs to solve PDEs on arbitrary manifolds is only now being considered and is the subject of this talk. We will review current methods and introduce a new technique that is loosely inspired by the Closest Point Method. This new technique, the Orthogonal Gradients Method (OGr), benefits from the advantages of using RBFs: the simplicity, the high accuracy but also the meshfree character, which gives the flexibility to represent the most complex geometries in any dimension.