Octree-mg

The octree-mg library implements parallel geometric multigrid methods on quadtree/octree grids, which can be used to solve elliptic PDEs such as Poissons's equation. The provided solvers can be used in existing adaptive-mesh-refinement (AMR) frameworks that employ quadtree/octree grids.

The code is described in detail in the publication A geometric multigrid library for quadtree/octree AMR grids coupled to MPI-AMRVAC, also available at arXiv.

Usage

Type make in the top folder, and run the programs in the tests folder.

Including the library in other projects

You can either include a full copy of octree-mg using e.g. git submodules of subtrees, or include it as a single Fortran module, see the folder single_module.

Features

• MPI parallelization
• The same code can be used in 2D/3D (compiled into two different libraries)
• Support for adaptively refined grids, with a consistent discretization near refinement boundaries
• Rectangular grids can easily be created (e.g. 512 x 256 x 256 cells).
• Operators with sparse stencils (5/7-point in 2D/3D) are supported
• Support for periodic, Dirichlet, Neumann, and continuous boundary conditions
• Coarse grids are automatically created

Restrictions

• One layer of ghost cells is used, and diagonal ghost cells are currently not set. This means stencils with diagonal elements are not possible.
• Point-wise smoothers are employed, so currently a requirement is that dx, dy and dz are similar

Using the free-space solver in MPI-AMRVAC

The "single-module" version of this library is included in MPI-AMRVAC, but it does not include the free-space module. An example of how to do this can be found under tests/multigrid/free_space_3d in the MPI-AMRVAC folder, see in particular the file local.make.