A compact radial basis function partition of unity method

In this work we develop the standard Hermite interpolation based RBF-generated finite difference (RBF-HFD) method into a new faster and more accurate technique based on partition of unity (PU) method. In the new approach, much fewer number of local linear systems needs to be solved for calculating the stencil weights. This reduces the computational cost of the method, remarkably. In addition, the method is flexible in using different types of PU weight functions, smooth or discontinuous, each results in a different scheme with additional nice properties. We also investigate the scaling property of polyharmonic spline (PHS) kernels to develop a simple and stable algorithm for computing local approximants in PU patches. Experimental results confirm the efficiency and applicability of the proposed method.

Automated summary

In this work, the standard Hermite interpolation based RBF-HFD method is developed into a new faster and more accurate technique based on the PU method. The new approach solves much fewer local linear systems for calculating stencil weights, reducing computational cost. The method also allows flexibility in using different types of PU weight functions and utilizes the scaling property of PHS kernels.