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.