Stable radial basis function interpolation for multi-physics simulation applications

Abstract

In multi-physics simulation applications there is a need for some kind of middleware between distinct simulations. The preCICE project ([4]) aims to provide such a software. One key component of this is to interpolate data from one mesh to another. There are several possibilities for doing this, however in this bachelor thesis I will primarily consider radial basis functions. These have several advantages like for instance being oblivious of topological information of the meshes, thus working on arbitrary point clouds, but also some drawbacks such as bad numerical stability. There is some parameter that can be tuned to trade interpolation accuracy against stability, but recent results showed that there is a way to get good numerical stability and good accuracy at the same time. This thesis will focus on this method for improving numerical stability, the RBF-QR method. An implementation is given in Python and C++ with the latter being able to be used in highly parallel applications.