2.4. Optional installation of PETSc/SLEPc

If you want to solve for eigenvalue problems, pyoomph by default will invoke scipy’s eigensolver based on ARPACK. However, for unsymmetric matrices which usually arise in complicated problems, SLEPc provides a much more stable alternative. So whenever you want to investigate linear stability, you should consider performing the following steps. The are all optional, but usually give better and more stable eigenvalue results. In any case, it is advised to occasionally check your eigenvalues by adding report_accuracy=True to calls of solve_eigenproblem(). We unfortunately do not really know how to install SLEPc on Windows, so you have to find your own way of installing it (and let us know the steps. A good start can be found here).

SLEPc depends on PETSc, so it is advisable to install both of these packages together. Also, since we often will obtain matrices with a zero on a diagonal (mainly due to Lagrange multipliers, incompressibilty constraints, etc.) we need a suitable linear solver backend in PETSc which can perform pivoting. We usually use MUMPS for that. Also, if you want to solve normal mode eigenvalue problems (cf. Section 10.3 and Section 10.4), we must have support for complex-valued eigenvalue problems, which requires to compile PETSc/SLEPc and MUMPS with complex values.

All three packages can be downloaded an installed together. On Mac with an M1 (arm64) chip, this must be again done in a Rosetta 2 terminal, at least if you want to use MKL Pardiso as linear solver (see previous pages).

We start by downloading PETSc in a folder of our choice (replace A_FOLDER_OF_YOUR_CHOICE in the following accordingly). If you have installed pyoomph in a python environment, it is advisable to also activate this environment now.

cd A_FOLDER_OF_YOUR_CHOICE
git clone -b release https://gitlab.com/petsc/petsc.git petsc
cd petsc

We know have to export some environment variables:

export PETSC_DIR=$(pwd)
export PETSC_ARCH=pyoomph_petsc_arch

Note that the choice of the name pyoomph_petsc_arch can be changed arbitrarily.

We then have to make sure that we have flex and Bison. On Ubuntu (and other Linux types analogously), you can install it system-wide via

sudo apt install flex bison

Alternatively, you can let PETSc download it as well by adding --download-bison at the end of the following configuration command. Note that we download and install further solver pacakges here, which are usually not needed, but likely will be used in future.

./configure --with-mpi  --with-petsc4py --download-mumps=yes --download-hypre=yes --download-parmetis=yes --download-ptscotch=yes --download-slepc=yes --download-superlu=yes --download-superlu_dist=yes --download-suitesparse=yes --download-metis=yes --download-scalapack --with-scalar-type=complex

You can also add optimization or OpenMP support, e.g. --with-debugging=0, -with-openmp, --with-openmp-kernels. For all details, please call ./configure --help.

Note

If you should have issues with cmake on Ubuntu (and potentially other distros), try

  1. Install cmake (updated version, see https://askubuntu.com/questions/355565/how-do-i-install-the-latest-version-of-cmake-from-the-command-line)

  2. add flag --download-fblasapack=1 when configuring

At the end of the configuration process, a make command will be written, which you have to execute as a next step.

Afterwards, PETSc/SLEPc is installed to the folder A_FOLDER_OF_YOUR_CHOICE/petsc/pyoomph_petsc_arch. At the end, it will also show a test command, by what you can test the basic functionality of of your installation.

To use it within pyoomph, you have to make sure that you always

export PETSC_DIR=A_FOLDER_OF_YOUR_CHOICE/petsc
export PETSC_ARCH=pyoomph_petsc_arch
export PYTHONPATH=$PYTHONPATH:$PETSC_DIR/$PETSC_ARCH/lib

It is advised to copy these statements into your .bashrc or .zshrc (depending on the terminal you use). Alternatively, if you use a python environment for pyoomph, you can also put these in the activate script of the environment. Note, however, that these won’t be unset automatically if you deactivate the environment then, only if you close the terminal.

To use SLEPc with MUMPS as eigensolver, either set it in python during your driver code, e.g.

problem.set_eigensolver("slepc").use_mumps()

or supply the flag --slepc_mumps when calling your driver code:

python my_eigenvalue_simulation.py --slepc_mumps