Abstract de la publi numéro 14226
Matrices coming from elliptic Partial Differential Equations (PDEs) have been shown to have
a low-rank property: well defined off-diagonal blocks of their Schur complements can be approximated by
low-rank products. Given a suitable ordering of the matrix which gives to the blocks a geometrical meaning,
such approximations can be computed using an SVD or a rank-revealing QR factorization. The resulting
representation offers a substantial reduction of the memory requirement and gives efficient ways to perform
many of the basic dense algebra operations.
Several strategies have been proposed to exploit this property. We propose a low-rank format called Block
Low-Rank (BLR), and explain how it can be used to reduce the memory footprint and the complexity of
direct solvers for sparse matrices based on the multifrontal method. We present experimental results that
show how the BLR format delivers gains that are comparable to those obtained with hierarchical formats such
as Hierarchical matrices (H matrices) and Hierarchically Semi-Separable (HSS matrices) but provides much
greater flexibility and ease of use which are essential in the context of a general purpose, algebraic solver.