One of the most time-consuming parts of our CFD framework QuICC is the computation of the physical to spectral space transformations. In spherical geometry, this transformation can be decomposed into three main parts: Fourier Transform and Spherical Harmonics Transform for angular parts and Jones-Worland Transform for the radial part. In this poster, we present a modern polynomial order connection approach for these calculations. It reformulates the complex polynomial transforms as FFTs through a sequence of order manipulations using well-established polynomial recurrence relations and Discrete Cosine Transforms (DCT), which in turn are calculated with the help of the VkFFT library. The recurrence relations are calculated as a sequence of bidiagonal matrix multiplications and backsolves implemented as a separate library called PfSolve. We also present the benchmark evaluation of the implemented algorithm against the common quadrature approach and evaluate the memory and accuracy gains. This benchmark is performed with the help of the testing suite of QuICC and will consider modern HPC solutions from both AMD and Nvidia due to the cross-platform support of the runtime code generation platform used for both PfSolve and VkFFT.