Abstract
A completely scalable parallel algorithm, the Parallel Multi-Layer Hybrid Block (PMHB) method, is proposed to solve block-tridiagonal equations on parallel computers. PMHB has multi-layers of parallelism. The different parallel tridiagonal solvers can be choused on different layers for different applications. By choosing different solvers on different layers and controlling its multi-layer partition, PMHB can deliver better performance for different applications on different machine ensembles and problem sizes. Theoretical analyses and numerical experiments indicate that PMHB is an efficient and arbitrarily extensible method with multi-layer hybrid cycle reduction calculation. The method has been implemented on the “Zi-Qiang 3000” supercomputer of Shanghai University. The numerical results are the same with the theoretical analysis. Given the accuracy, the linear speedup rate is obtained, and parallel efficiency over 90 % is reached.
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