TITLE:
Schur Complement Computations in Intel® Math Kernel Library PARDISO
AUTHORS:
Alexander Kalinkin, Anton Anders, Roman Anders
KEYWORDS:
Multifrontal Method, Direct Method, Sparse Linear System, Schur Complement, HPC, Intel® MKL
JOURNAL NAME:
Applied Mathematics,
Vol.6 No.2,
February
5,
2015
ABSTRACT: This paper describes a method of calculating the Schur complement of a sparse positive definite matrix A. The main idea of this approach is to represent matrix A in the form of an elimination tree using a reordering algorithm like METIS and putting columns/rows for which the Schur complement is needed into the top node of the elimination tree. Any problem with a degenerate part of the initial matrix can be resolved with the help of iterative refinement. The proposed approach is close to the “multifrontal” one which was implemented by Ian Duff and others in 1980s. Schur complement computations described in this paper are available in Intel® Math Kernel Library (Intel® MKL). In this paper we present the algorithm for Schur complement computations, experiments that demonstrate a negligible increase in the number of elements in the factored matrix, and comparison with existing alternatives.