A Robust Algebraic Domain Decomposition Preconditioner for Sparse Normal Equations
A parallel implementation of the preconditioner suitably interfaced with the PETSc library.
The code available in this repository can reproduce the results from the following paper.
@article{aldaas2021robust,
Author = {Al Daas, Hussam and Jolivet, Pierre and Scott, Jennifer A.},
Title = {A Robust Algebraic Domain Decomposition Preconditioner for Sparse Normal Equations},
Year = {2022},
Journal = {SIAM Journal on Scientific Computing},
Pages = {A1047--A1068},
Volume = {44},
Issue = {3},
Url = {https://github.com/prj-/aldaas2021robust}
}
Getting started
Dependencies
Make sure you have access to a recent PETSc installation (version 3.18.0 or above), configured with the options --download-slepc --download-hpddm, using 32-bit indices, double-precision real-valued scalars (--with-64-bit-indices=0 --with-precision=double --with-scalar-type=real).
Then, after setting the appropriate environment variable ${PETSC_DIR} and ${PETSC_ARCH} compile the single C source file from the repository with the following command.
$ make sparse_ls
When using Fortran, the above command should read make sparse_ls_f instead.
When using Python, make sure that petsc4py is visible in your environment variable ${PYTHONPATH}, e.g., PYTHONPATH=${PYTHONPATH}:${PETSC_DIR}/${PETSC_ARCH}/lib.
Usage example
One should be able to launch the following commands, which solve respectively the linear least-squares problems associated to mesh_deform and lp_stocfor3 from the SuiteSparse Matrix Collection.
$ mpirun -np 4 ./sparse_ls -mat_name datafiles/mesh_deform.dat -options_file default.rc -pc_type hpddm
$ mpirun -np 4 ./sparse_ls -mat_name datafiles/lp_stocfor3.dat -options_file default.rc -pc_type hpddm
The command line option -pc_type may also be set to asm, hypre (if PETSc has been configured with --download-hypre), gamg, qr (if configured with --download-suitesparse), or whatever the user feels like trying out.
All the other matrices are available at the following URL: http://joliv.et/aldaas2021robust/mat_name.ext, where mat_name is any of the identifier from the paper, and ext is either dat (PETSc binary format) or mat (MATLAB binary format).
Here are two examples: http://joliv.et/aldaas2021robust/Hardesty2.dat and http://joliv.et/aldaas2021robust/cont11_l.mat. Matrices supplied through the command-line option -mat_name must always be in PETSc binary format. .mat files are merely provided for an easier inspection in MATLAB, e.g., using the spy command.