The Scheduling of a Parallel Tiled Matrix Inversion Algorithm

The non equilibrium Green’s function method used in density functional theory based methods for computing electron transport at nano scale requires repeated inversions of a large block tridiagonal matrix. This calculation constitutes a substantial part of the total execution time, and therefore an efficient special method for the block tridiagonal matrix inversion was developed recently. This paper presents an efficient parallel implementation of the new method based on tiling of the matrix blocks and a near optimal scheduling of the computational kernels operating on the tiles. Although aimed at the solution of a rather special problem, the presented techniques have much broader applications.