Elisabeth Larsson: Radial basis function partition of unity methods for elliptic and parabolic PDEs

Numerical methods for realistic simulation problems need to be computationally efficient and flexible with respect to the problem properties. For problems that can be mathematically modeled by partial differential equations (PDEs), methods based on radial basis function (RBF) approximation are of interest because they are flexible with respect to the geometry and the type of PDE. They can also provide high order approximations to sufficiently smooth functions. However, high order does not necessarily imply computational efficiency. The computational cost of RBF methods employing global approximations is in many cases too high. In this talk, RBF approximation is combined with a partition of unity approach to reduce computational cost. Theoretical and numerical results demonstrate that the method has potential to be competitive.