RBF-generated Finite Differences for Elliptic PDEs on Multiple GPUs
Radial Basis Functions (RBFs) provide a powerful and elegant solution to calculate weights for generalized Finite Differences on arbitrary node distributions. Weights apply to stencils of scattered nodes (e.g., Figure 1) and result in a derivative approximation at the stencil center. High-order accuracy is easily achieved by increasing the number of nodes per stencil. differentiation weights to approximate a derivative at the center (black square).
This effort extends previous work on a multi-CPU/GPU implementation of RBF-FD originally dedicated to explicit solutions of hyperbolic PDEs . The addition of a GPU-based implicit solver for elliptic PDEs completes the necessary building blocks required for large-scale GPU solution of geophysical flows based entirely on the RBF-FD method.