A trivariate interpolation algorithm using a cube-partition searching procedure
For researchers needing fast and accurate trivariate interpolation with large numbers of nodes, this algorithm offers an efficient solution.
The paper proposes a fast trivariate interpolation algorithm using a cube-partition searching procedure to efficiently handle large datasets, achieving high efficiency and accuracy as shown by complexity analysis and numerical experiments.
In this paper we propose a fast algorithm for trivariate interpolation, which is based on the partition of unity method for constructing a global interpolant by blending local radial basis function interpolants and using locally supported weight functions. The partition of unity algorithm is efficiently implemented and optimized by connecting the method with an effective cube-partition searching procedure. More precisely, we construct a cube structure, which partitions the domain and strictly depends on the size of its subdomains, so that the new searching procedure and, accordingly, the resulting algorithm enable us to efficiently deal with a large number of nodes. Complexity analysis and numerical experiments show high efficiency and accuracy of the proposed interpolation algorithm.