Hierarchical Matrix Techniques on Massively Parallel Computers

Hierarchical matrix (H-matrix) techniques can be used to efficiently treat dense matrices. With an H-matrix, the storage requirements and performing all fundamental operations, namely matrix-vector multiplication, matrix-matrix multiplication and matrix inversion can be done in almost linear complexity. In this work, we tried to gain even further speedup for the H-matrix arithmetic by utilizing multiple processors. Our approach towards an H-matrix distribution relies on the splitting of the index set. The main results achieved in this work based on the index-wise H-distribution are: A highly scalable algorithm for the H-matrix truncation and matrix-vector multiplication, a scalable algorithm for the H-matrix matrix multiplication, a limited scalable algorithm for the H-matrix inversion for a large number of processors