disco4est (abbrev. d4est) is a scalable hp-adaptive discontinuous Galerkin solver for non-linear elliptic partial differential equations on curved multi-block meshes.

Solver Details

• The discontinuous Galerkin method is used to discretize the non-linear or linear elliptic PDEs.

• We use an in-house hp-multigrid algorithm to precondition PETSc solvers. It uses surrogate levels to keep meshes 2:1 balanced.

• The multigrid algorithm can handle different smoothers (Chebyshev, Additive Schwarz... ) and different bottom solvers (p-multigrid, Krylov, ...).

• hp-adaptive mesh-refinement is used to efficiently converge on a solution.

• Different topologies and parallel mesh refinement is handled using the multi-block tree code p4est.

• Scaling of the multigrid solver has been tested up to O(10,000) cores.

Prerequisites

The dependencies are MPI, OpenBLAS, HDF5, PETSc, zlib, zlog and p4est. You will need at least MPI. If you do not have zlib, zlog, PETSc p4est, HDF5 or OpenBLAS, then these come bundled, so they will be installed automatically to the local build folder unless you specify otherwise.

On Mac OS X, you may simply install most dependencies through Homebrew:

brew install openblas hdf5 gperftools zlib

Just remember that the OS X system gcc is just a clang wrapper, so make sure to set the CC and CXX environment variables to e.g. gcc-7 and g++-7, with gcc (along with its bundled gfortran) installed through Homebrew. Also make sure your MPI installation wraps the same gcc, e.g. through brew install mpich --cc=gcc-7.

Note that due to a bug in the syslog headers in OS X 10.13 (High Sierra) you should provide the flag mmacosx-version-min, such as in export CC="gcc-7 -mmacosx-version-min=10.12" to compile zlog.

Installation

1. git clone --recursive https://github.com/trevor-vincent/d4est && cd d4est

2. Duplicate one of the Support/CMake/machine.cmake.*.example build configuration files to Support/CMake/machine.cmake and modify it to fit the local machine.

• Adjust the CMAKE_BUILD_TYPE variable to Release for (much faster) production builds.
• If you choose to use the bundled libraries, then these will be located in the build directory and will be compiled only once, unless you change cmake commandline options or delete the build directory.
• The cmake script searches for the MPI build on your system, so this never needs to be specified.
• There is a preconfigured example file for the Minerva cluster. On Minerva, also source Support/Scripts/build.env.minerva.example to configure the build environment, or duplicate and modify the file first.

3. Compile:

mkdir build && cd build
cmake ..
make -j4 # or adjust number of cores

4. Run an example:

cd ConstantDensityStar
mpirun -np 4 path/to/build/ConstantDensityStar/constant_density_star_driver

For the example to complete in O(10s) you may want to consult the options.input file to set amr.num_of_amr_steps=1.

On a cluster, refer to the Support/Scripts/submit.*.*.example files for guidance.

Options documentation

Configuration options are loaded from an options.input file residing in the same directory as the problem executable by default, or from the file supplied as the first positional command line argument.

• [problem]: Problem-specific options.
• [initial_mesh]
  • min_quadrants
  • min_level: Number of initial mesh refinements.
  • fill_uniform
  • regionX_deg: Initial polynomial degree in region X.
  • regionX_deg_quad_inc: Initial quadrature polynomial degree increment in region X.
• [amr]
  • scheme can be one of the following AMR refinement schemes:
    • uniform_h: Divides each element into 4 sub-elements in 2 dimensions, or into 8 sub-elements in 3 dimension.
    • uniform_p: Increases the polynomial order on each element by 1.
    • smooth_pred: hp-amr scheme that uses estimator performance to determine h or p refinement
  • num_of_amr_steps
  • max_degree

Licenses

This project is licensed under the GPLv2 License - see the LICENSE.md file for details
The logo is licensed under a Creative Commons License.

The disco-ball in the logo is a modified version of a design by Daouna Jeong from the Noun Project and the tree in the logo is a modified version of a design created by Musket from the Noun Project.

Authors

If you are doing research using disco4est, please cite our paper:

@article{PhysRevD.100.084052,
  title = {hp-adaptive discontinuous Galerkin solver for elliptic equations in numerical relativity},
  author = {Vincent, Trevor and Pfeiffer, Harald P. and Fischer, Nils L.},
  journal = {Phys. Rev. D},
  volume = {100},
  issue = {8},
  pages = {084052},
  numpages = {22},
  year = {2019},
  month = {Oct},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevD.100.084052},
  url = {https://link.aps.org/doi/10.1103/PhysRevD.100.084052}
}