Parallel Numerical Solution of ABD and BABD linear systems arising from BVPs

Abstract

We consider linear systems with coefficient matrices having the ABD or
the Bordered ABD (BABD) structures. These systems arise in the discretization
of BVPs for ordinary and partial differential equations with
separated and non-separated boundary conditions, respectively.
We describe the cyclic reduction algorithm for the solution
of BABD linear systems which allowed us to write the codes BABDCR and GBABDCR
(the latter code is suitable for matrices with a more generic BABD structure).
A comparison of the GBABDCR code with respect to the well-known sequential code
COLROW on ABD linear systems is then analysed.
We report some tests on an OpenMP Fortran 90 parallel version of the
GBABDCR code and finally we discuss about the use
of GBABDCR inside the BVP code BVPSOLVER.