SC Colloquium: "Radial Basis Function-Generated Finite Differences (RBF-FD): New Opportunities for Applications in Scientific Computing"
Radial Basis Function-generated Finite Differences (RBF-FD), a novel mesh-free method, has the ease of classical FD, yet combines high levels of accuracy with complete geometric flexibility, essential for both local refinement and to accurately handle irregular boundaries/surfaces. Furthermore, algorithmic complexity does not increase with dimension and the method inherently lends itself to short simple codes. It is also highly competitive compared to other state-of-the-art numerical methods. In recent benchmarking tests on the three dominant architectures composing high-performance computing systems today, Intel Multicore, Manycore and Nvidia GPUs, it has demonstrated excellent performance due to the very sparse compact structure of its differentiation matrices. In this presentation, we highlight some recent RBF-FD calculations.