Fast algorithm for solving fractional Helmholtz equation with spectral fractional Laplacian

This paper presents fast and accurate numerical methods for solving multi-dimensional fractional Helmholtz equation using spectral fractional Laplacian. By Dunford-Taylor integral representation of spectral fractional Laplacian, tensorial methods based on matrix transform technique can be used to discretize fractional Helmholtz equation. Our scheme can exactly solve system of equations using discrete sine transform, and it can significantly save computation cost and memory. To reveal the accuracy and efficiency of the suggested fast algorithms, two numerical tests are offered.