Architecture

The multigrid solvers consist of two ingredients: a Python-API and a set of C++ tools. The C++ tools use Peano's tarch and the matrixfree toolbox. Overall, the multigrid solvers realise the blueprint of Peano's application architecture. They focus, as stand-alone applications, on stationary, elliptic problems that materialise in

\( A x = b \)

With the stand-along multigrid solvers, they all realise the following pattern:

1. There is a multigrid project, which serves as a container or general wrapper. and defines the core multigrid solver steps.
2. The project hosts one or multiple solvers for a particular partial differential equation.
3. The multigrid is basically a factory producing a plain Peano 4 Python representation of the code.
4. The Peano 4 Python project then finally produces the C++ code.

The multigrid project defines what is to be solved and how (in terms of numerics). The Peano 4 project then represents how this is realised in principle, i.e. it accommodates a Python representation of all data models and computational steps. The C++ outcome is the actual realisation.

File conventions

Each multigrid solver is represented by one instance of petsc.solvers.Solver. Please consult this class' documentation for available subclasses (solver flavours) and information about files that are generated.