Monotone Multivariate Interpolation of Scattered Data Using Nested Hypercubes

One-dimensional linear interpolation is extended to arbitrary dimensions and scattered data using nested hypercubes. This is targeted at the evaluation of aerodynamic performance data in trajectory simulations and the generation of multi-fidelity response surfaces, though the approach is general. The algorithm demonstrates logarithmic scaling and quadratic convergence for regular and scattered interpolation centers. The performance for synthetic aerodynamic data, including steep gradients near the sonic line, is also provided. The efficiency of multithreaded parallel implementations in a shared-memory arena, including the use of graphical processing units, is demonstrated. Nomenclature φ radial basis function d dimensions of the parameter space m number of functionals n number of interpolation centers p number of partitions