Efficient vector-valued precorrected-FFT implementations

Develop efficient implementations of the kernel-independent precorrected-FFT algorithm for vector-valued problems, including the vector-valued problems considered by Tissari and Rahola, to offset their additional computational cost.

Background

The paper develops and tests a kernel-independent precorrected-FFT method for scalar-valued kernels, using proxy shells to construct spreading operators and accelerate nonstandard kernel summations. The authors note that their current work does not address vector-valued kernels or problems, although they expect the algorithm to extend to that setting. They identify the development of efficient implementations for such problems as unresolved, partly because vector-valued formulations incur additional computational cost. GPU implementations are mentioned as a possible way to mitigate this cost, but the concrete open issue is the efficient implementation of the vector-valued extension.