Memory Aware Poisson Solver for Peta-Scale Simulations with one FFT Diagonalizable Direction

Problems with some sort of divergence constraint are found in many disciplines: computational fluid dynamics, linear elasticity and electrostatics are examples thereof. Such a constraint leads to a Poisson equation which usually is one of the most computationally intensive parts of scientific simulation codes. In this work, we present a memory aware Poisson solver for problems with one Fourier diagonalizable direction. This diagonalization decomposes the original 3D system into a set of independent 2D subsystems. The proposed algorithm focuses on optimizing the memory allocations and transactions by taking into account redundancies on such 2D subsystems. Moreover, we also take advantage of the uniformity of the solver through the periodic direction for its vectorization. Additionally, our novel approach automatically optimizes the choice of the preconditioner used for the solution of each frequency subsystem and dynamically balances its parallel distribution. Altogether constitutes a highly efficient and robust HPC Poisson solver that has been successfully attested up to 16384 CPU-cores.