Two-dimensional interpolation using a cell-based searching procedure

TL;DR

This paper introduces an efficient bivariate interpolation algorithm that uses a cell-based search procedure and partition of unity with radial basis functions to improve computational speed and performance.

Contribution

It presents a novel cell-based searching method combined with partition of unity for efficient 2D interpolation, reducing CPU time significantly.

Findings

Reduced computational time demonstrated through numerical experiments

Effective partitioning of the domain enhances search efficiency

Algorithm outperforms traditional methods in speed and accuracy

Abstract

In this paper we present an efficient algorithm for bivariate interpolation, which is based on the use of the partition of unity method for constructing a global interpolant. It is obtained by combining local radial basis function interpolants with locally supported weight functions. In particular, this interpolation scheme is characterized by the construction of a suitable partition of the domain in cells so that the cell structure strictly depends on the dimension of its subdomains. This fact allows us to construct an efficient cell-based searching procedure, which provides a significant reduction of CPU times. Complexity analysis and numerical results show such improvements on the algorithm performances.