A versatile parallel block-tridiagonal solver for spectral codes

Three-dimensional (3-D) processor configuration of a parallel solver is introduced to solve a massive block-tridiagonal matrix system in this paper. The purpose of the added parallelization dimension is to retard the saturation of the scaling due to communication overhead and an inefficient parallelization. The semi-empirical formula for the matrix operation count of the typical parallel algorithms is estimated including the saturation effect in 3-D processor grid. As the most suitable algorithm, the combined method of “Divide-and-Conquer” and “Cyclic Odd-Even Reduction” is implemented in a MPI-Fortran90 based numerical code named TORIC. The new 3-D parallel solver of TORIC using thousands of processors shows about 4 times improved computation speed at the optimized 3-D grid than the old 2-D parallel solver in the same condition.