The application of the operators [.bar.R] : [??} [right arrow] W and R : [V.sup.h] [right arrow] W on [??] and [.bar.b], respectively, are implemented using PETSc
's VecScatter class.
The fully-vectorial MR-FEM-CSI algorithm has been implemented in C/C++ for distributed memory systems using MPI under the PETSc
Release 3.0 of PETSc
is the only package with a parallel mesh management system that is fully integrated and can utilize the powerful algebraic solvers in PETSc
and Aztec approaches, object-oriented design methodologies are at the basis of the Diffpack project [Bruaset and Langtangen 1997].
 --, PCBBDC: dual-primal preconditioners in PETSc
, Talk at the Conference: Celebrating 20 Years of Computational Science with PETSc
, June 2015.
All algorithms were implemented in C/C++ linked with the Intel Math Kernel  and PETSc
 libraries, compiled under the Intel MPI compiler using the -O3 optimization level.
7: Iteratively solve the system using either the KSP AGMRES (Algorithm 1) or the PETSc
built-in KSP GMRES [41, Algorithm 4].
Knyazev, Preconditioned eigensolver LOBPCG in hypre and PETSc
, in Proceedings of the 16th International Conference on Domain Decomposition Methods 2005, O.
It is worth noting here that, despite all the different optimization strategies, sparse matrix products are still not standard in sparse libraries such as PETSc
SMITH, Making automatic differentiation truly automatic: coupling PETSc
with ADIC, Future Generation Computer Systems, 21 (2005), pp.
TT to obtain the finite element discretization and PETSc
for the numerical linear algebra (routines for matrix-vector multiplication, scalar products, etc.).
The Portable, Extensible Toolkit for Scientific computation (PETSc
)  is used for the parallel implementation and all numerical results are obtained on a cluster of PCs running Linux.