Scalable parallel linear solver for compact banded systems on heterogeneous architectures

A scalable algorithm for solving compact banded linear systems on distributed memory architectures is presented. The proposed method factorizes the original system into two levels of hierarchies, and solves it using parallel cyclic reduction both shared memory. This has a lower communication footprint across partitions compared to conventional algorithms involving data transposes or re-partitioning. developed in this work generalized with flexible decompositions. For systems, direct solver deterministic operation counts depending matrix size, its bandwidth, partition strategy. implementation runtime configuration details are discussed performance optimization. Scalability demonstrated as well representative fluid mechanics application problem, which dominant computational cost tridiagonal numerical schemes 3D periodic domain. particularly useful arising from finite difference operators wide range partial differential equation problems, such but not limited simulations compressible turbulent flows, aeroacoustics, elastic–plastic wave propagation, electromagnetics. It alleviates obstacles their use modern high computing hardware, where power nodes multi-threaded processing units.