Vico-Greengard-Ferrando quadratures in the tensor solver for integral equations
This work provides an efficient tensor-based method for solving integral equations, benefiting computational scientists who need fast and accurate convolution computations.
The authors develop a low-rank tensor implementation of Vico-Greengard-Ferrando quadratures for computing convolutions with Green's functions, achieving spectral accuracy using only FFT and QTT decomposition.
Convolution with Green's function of a differential operator appears in a lot of applications e.g. Lippmann-Schwinger integral equation. Algorithms for computing such are usually non-trivial and require non-uniform mesh. However, recently Vico, Greengard and Ferrando developed method for computing convolution with smooth functions with compact support with spectral accuracy, requiring nothing more than Fast Fourier Transform (FFT). Their approach is very suitable for the low-rank tensor implementation which we develop using Quantized Tensor Train (QTT) decomposition.