Methods to utilize SIMT and SIMD instruction level parallelism in tridiagonal solvers

The most widely used parallel architectures in today's High Performance Computing systems utilize multi-core CPUs, many-core GPUs or Intel's MIC (Many Integrated Core). The effort of new algorithm and implementation development greatly influences the performance on these architectures, and the differences between their underlying ILP parallelism - namely SIMT (Single Instruction Multiple Thread) and SIMD (Single Instruction Multiple Data) - require different approaches. The aim of the work to be presented is to show how high performance can be achieved in solving multiple scalar- and block-tridiagonal system of equations. The Thomas algorithm is implemented on all three hardware platforms, and for the GPU we also implement a hybrid algorithm based on Parallel Cyclic Reduction and Thomas algorithm for solving scalar problem and a thread level, work-sharing based algorithm for block-tridiagonal problems. Performance comparisons and a discussion on efficiency are also included.