Место издания: Тверь , Год издания: 2017

We present a MPI based direct solver for a system of linear equations that arise as finite difference approximations of a boundary value problem for the 3D Helmholtz equation with Perfectly Matched Layers. The solver uses data compression (Low Rank approximation and Hierarchically Semi Separable formats for storing intermediate data) to reduce memory consumption and improve performance. For good scalability of the solver, factorization of matrix columns that correspond to the middle level of the elimination tree is combined with computations of Schur complements at the highest level of the elimination tree. This trick helps to achieve scalability close to ideal for up to 16 cluster nodes though results are not so impressive on bigger clusters.