Igor Tominec
Division of Scientific Computing, Department of Information Technology, Uppsala University
Methods for solving elliptic partial differential equations based on radial basis functions (RBFs) in a collocation setup are prone to instabilities in the presence of Neumann boundary conditions. This is unfortunate since such conditions are important to use when for example constructing a mechanical model of the human diaphragm. We solve this issue by formulating the RBF finite difference method in a least-squares setup instead. The change of the residual minimization framework allowed the convergence under node refinement and allowed us to further develop the method to support a trial space which does not conform to the geometry on which the differential equation is solved.