OVERVIEW

petsc4m-lite is an interface of PETSc for MATLAB and GNU Octave on Linux or MacOSX. Its main top-level function is petscSolve, which uses the direct solver MUMPS by default but can be configured to call any combination of solves and preconditioners available in PETSc. For convenience, petsc4m-lite provides two additional top-level functions, gmresILU and gmresHypre, which use ILU0 and BoomerAMG as right preconditioners, respectively. In all cases, the true residuals are used for the convergence criteria. The inputs matrices can be either a MATLAB sparse matrix or a CRS struct containing row_ptr, col_ind, and vals fields.

EXAMPLE

The following example illustrates how to use gmresILU:

  A = gallery('wathen', 10, 10);
  b = A * ones(length(A), 1);
  rtol = 10*eps(class(PetscReal(0))).^(1/2);
  [x,flag,relres,iter,reshis,times] = gmresILU(A, b, [], rtol);

SETTING UP PETSC4M-LITE

petsc4m-lite requires PETSc. A recommended approach for installing PETSc is to use miniconda3 (or anaconda3), since it has the most up-to-date version of PETSc. Suppose you have already installed either miniconda3 or anaconda3 and have conda in the path and the environment variable CONDA_PREFIX pointing to the correct version, you can install PETSc using the command

   conda install -y -c conda-forge petsc=3.18.1

On Linux systems, you can also use the older versions of PETSc that comes with your Linux distribution if you have system-administration access. For example, on Ubuntu 22.04, you can install PETSc using the command

  sudo apt update
  sudo apt install -y petsc-dev

Of course, you can also install PETSc yourself and define the environnement variable PETSC_DIR. petsc-lite tries to locate the PETSc installation in the following order:

1. root path of PETSc specified by the environment variable PETSC_DIR;
2. installation with Anaconda/Miniconda with environment variable CONDA_PREFIX;
3. System installation under /usr/lib/petsc (such as on Ubuntu).

NOTES ON PETSC4M-LITE IN MATLAB

When running MATLAB on Linux or with JAVA enabled, petsc4m-lite pass data through files between MATLAB and PETSc for robustness. However, on MacOSX, data will be passed through memory when MATLAB is started without Java using the command

matlab -nojvm

This may be better for solving large systems. On Linux systems, unfortunately, your only option would be to use Octave (see below).

NOTES ON PETSC4M-LITE IN OCTAVE

petsc4m-lite works with Octave on Linux and Mac. In this case, data is passed through memory. It is recommended that you install Octave using Miniconda.

AUTHOR and CITATION

petsc4m-lite was developed and maintained by Xiangmin (Jim) Jiao [email protected]. It was mainly used for comparative research. If you found the software useful, please cite the following paper.

@article{ghai2019comparison, title={A comparison of preconditioned Krylov subspace methods for large-scale nonsymmetric linear systems}, author={Ghai, Aditi and Lu, Cao and Jiao, Xiangmin}, journal={Numerical Linear Algebra with Applications}, volume={26}, number={1}, pages={e2215}, year={2019}, publisher={Wiley Online Library} }