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Dr. Bengt Fornberg and Dr. Natasha Flyer present "Radial Basis Functions: Freedom from meshes in scientific computing". Please join us for refreshments at 2:45 p.m.
Finite difference (FD) methods were first used for solving PDEs over a century ago. FD stencils have typically been based on Cartesian grids, requiring the results to be exact for polynomials of as high degree as permitted by the stencil size. When the polynomials are either supplemented with or altogether replaced by radial basis functions (RBFs), grids become unnecessary & the node points can be scattered as needed. Such RBF-FD approximations combine high levels of accuracy w/ much improved geometric flexibility, essential both for local refinement and to accurately handle irregular boundaries and material interfaces. Additional benefits include high computational efficiency, short and simple codes, and excellent opportunities for distributed computing. We will in this presentation highlight some recent RBF-FD calculations, mostly from the geosciences.
Bengt Fornberg (Ph.D. Uppsala Univ., Sweden) faculty of Applied Mathematics at Univ. of Colo., Boulder since 1995. Preceded by positions at the European Org. for Nuclear Research, Calif. Inst. of Technology, and Exxon Corporate Research. His research focuses on numerical methods for solving PDEs and computational methodologies for analytic functions.
Natasha Flyer (Ph.D., Univ. of Michigan) is a staff scientist at NCAR in Boulder. Her research interests include development of computational methods for solar physics and geosciences and hybrid analytical-numerical methods for the solution of PDEs with singularities.