A Fast Algorithm for Aperiodic Linear Stencil Computation using Fast Fourier Transforms

Stencil computations are widely used to simulate the change of state physical systems across a multidimensional grid over multiple timesteps. The state-of-the-art techniques in this area fall into three groups: cache-aware tiled looping algorithms, cache-oblivious divide-and-conquer trapezoidal and Krylov subspace methods. In paper, we present two efficient parallel algorithms for performing linear stencil computations. Current direct solvers domain computationally inefficient, methods require manual labor mathematical training. We solve these problems stencils by using DFT preconditioning on method achieve solver which is both fast general. Indeed, while all currently available solving general perform Θ ( NT ) work, where N size spatial T number timesteps, our o work. To best knowledge, give first that use Fourier transforms compute final data evolving initial many timesteps at once. Our handle periodic aperiodic boundary conditions, polynomially better performance bounds (i.e., computational complexity runtime) than other existing solutions. Initial experimental results show implementations evolve grids roughly 10 7 cells around 5 run orders magnitude faster problems, 1.3 × 8.5 problems. Code Repository: https://github.com/TEAlab/FFTStencils