Tridigpu: A GPU Library for Block Tridiagonal and Banded Linear Equation Systems

In this article, we present a CUDA library with a C API for solving block cyclic tridiagonal and banded systems on one GPU. The library can process block tridiagonal systems with block sizes from 1 × 1 (scalar) to 4 × 4 and banded systems with up to four sub- and superdiagonals. For the compute-intensive block size cases and cases with many right-hand sides, we write out an explicit factorization to memory; however, for the scalar case, the fastest approach is to only output the coarse system and recompute the factorization. Prominent features of the library are (scaled) partial pivoting for improved numeric stability; highest-performance kernels, which completely utilize GPU memory bandwidth; and support for multiple sparse or dense right-hand side and solution vectors. The additional memory consumption is only 5% of the original tridiagonal system, which enables the solution of systems up to GPU memory size. The performance of the state-of-the-art scalar tridiagonal solver of cuSPARSE is outperformed by factor 5 for large problem sizes of 225 unknowns, on a GeForce RTX 2080 Ti.