GMGPolar

GMGPolar is a performant geometric multigrid solver using implicit extrapolation to raise the convergence order. It is based on meshes in tensor- or product-format. GMGPolar's focus applications are geometries that can be described by polar or curvilinear coordinates for which suited smoothing procedures have been developed.

If using GMGPolar, please cite:

M. J. Kühn, C. Kruse, U. Rüde. Implicitly extrapolated geometric multigrid on disk-like domains for the gyrokinetic Poisson equation from fusion plasma applications. Journal of Scientific Computing, 91 (28). Springer (2022). Link: https://link.springer.com/article/10.1007/s10915-022-01802-1

Tested plateforms

Working

• Linux x86_64 with GNU 9.3.0 compilers.

Obtaining the source code

The GmgPolar Solver does not require any external libraries. It is possible to link the code with the sparse direct solver MUMPS.

• MUMPS is optional. However, it is absolutely recommended if large grids are considered. Otherwise, the nonoptimal backup solver will be used for factorization of the matrices and will slow down the setup phase significantly. To use it, compile the code with option -DGMGPOLAR_USE_MUMPS. It is recommended to use the latest version (currently 5.4.1) but any version ulterior to 5.1.0 should be okay. MUMPS is available freely on demand on the MUMPS consortium website "mumps-solver.org".

The installation can be done by typing the following commands in your terminal

# download the latest stable version
# it will create a directory named GMGPolar

git clone https://github.com/mknaranja/GMGPolar

Now that everything is ready, we can compile the solver. Edit the file Makefile.in so that it reflects your configuration (path to libraries, file names, etc).

Building the library

The build process is done using CMake:

# Create build directory
mkdir -p build && cd build
# Configure
cmake ..
# Build
cmake --build .

Currently, the default build process only supports gnu compiler although Intel compiler has been successfully tested for some configurations.

Running GmgPolar

You can run the solver without having to write a code (as we do in the next section). After building the library, a binary is created called ./build/gmgpolar_simulation, it takes parameters directly from command-line.

# To try GmgPolar on a small problem size, without having to write any code,
# ./build/gmgpolar_simulation uses default parameters with a grid 49 x 64.

./build/gmgpolar_simulation

# For more details on the available parameters, see the main.cpp source code.
# You can control the number of OpenMP threads used by changing the environment variable.
# Note that only MUMPS is parallelized at the moment.

export OMP_NUM_THREADS=4

Executing an example

Once the library is built, you can run the examples:

# the verbose option defines the extent of the output

./build/gmgpolar_simulation --verbose 2

# the option --debug 1 turns on internal debugging and compares the results of the C++ code 
# with the results from the previous matlab implementation.

./build/gmgpolar_simulation --debug 1

Issue tracker

If you find any bug, didn't understand a step in the documentation, or if you have a feature request, submit your issue on our Issue Tracker: https://github.com/mknaranja/GMGPolar/issues by giving:

• reproducible parameters
• computing environment (compiler, etc.)

Release Notes

• GmgPolar 1.0

1. Working multigrid cycle

2. In-house solver and possibility to link with MUMPS for the smoothing and coarse grid solution

3. Extrapolation strategies:

   a. No extrapolation (--extrapolation 0)

   b. Default implicit extrapolation (--extrapolation 1)

   c. Non-default implicit extrapolation with smoothing of all nodes on the finest level [experimental, use with care, convergence cannot be observed with residual] (--extrapolation 2)

4. Optimization of apply_A / build_rhs / apply_prolongation / build_Asc / apply_Asc_ortho