Least Squares Radial Basis Function Partition of Unity Method

Victor Shcherbakov
Division of Scientific Computing
Department of Information Technology
Uppsala University
Uppsala

Abstract:

In this work we develop a radial basis function partition of unity method for solving partial differential equations. Instead of pure collocation, that formerly was commonly used together with radial basis function methods, we adopt a least squares approach. This allows to reduce the sensitivity of approximation to the node point locations. Also we use precomputed templates for the partitions, that allows to avoid some calculations, which were necessary in the pure collocation case. Thus, the least squares radial basis function partition of unity methods becomes a more robust and computationally more efficient tool for solving partial differential equations.