A Fast Solver for Large Tridiagonal Systems on Multi-Core Processors (Lass Library)

Many problems of industrial and scientific interest require the solving of tridiagonal linear systems. This paper presents several implementations for the parallel solving of large tridiagonal systems on multi-core architectures, using the OmpSs programming model. The strategy used for the parallelization is based on the combination of two different existing algorithms, PCR and Thomas. The Thomas algorithm, which cannot be parallelized, requires the fewest number of floating point operations. The PCR algorithm is the most popular parallel method, but it is more computationally expensive than Thomas. The method proposed in this paper starts applying the PCR algorithm to break down one large tridiagonal system into a set of smaller and independent ones. In a second step, these independent systems are concurrently solved using Thomas. The paper also contains an analytical study of which is the best point to switch from PCR to Thomas. Also, the paper addresses the main performance issues of combining PCR and Thomas proposing a set of alternative implementations, some of them even imply algorithmic changes. The performance evaluation shows that the best implementation achieves a peak speedup of 4 with respect to the Intel MKL counterpart routine and 2.5 with respect to a single-threaded Thomas.