Mesh refinement criteria

Despite research since the mid-1980s, it isn’t completely clear how to refine meshes for complex situations like the ones modeled by ASPECT. The basic problem is that mesh refinement criteria either can refine based on some variable such as the temperature, the pressure, the velocity, or a compositional field, but that oftentimes this by itself is not quite what one wants. For example, we know that Earth has discontinuities, e.g., at 440km and 610km depth. In these places, densities and other material properties suddenly change. Their resolution in computation models is important as we know that they affect convection patterns. At the same time, there is only a small effect on the primary variables in a computation – maybe a jump in the second or third derivative, for example, but not a discontinuity that would be clear to see. As a consequence, automatic refinement criteria do not always refine these interfaces as well as necessary.

To alleviate this, ASPECT has plugins for mesh refinement. Through the parameters in Parameter name: Strategy, one can select when to refine but also which refinement criteria should be used and how they should be combined if multiple refinement criteria are selected. Furthermore, through the usual plugin mechanism, one can extend the list of available mesh refinement criteria (see the parameter “Strategy” in Parameter name: Strategy). Each such plugin is responsible for producing a vector of values (one per active cell on the current processor, though only those values for cells that the current processor owns are used) with an indicator of how badly this cell needs to be refined: large values mean that the cell should be refined, small values that the cell may be coarsened away.

To implement a new mesh refinement criterion, you need to overload the aspect::MeshRefinement::Interface class and use the ASPECT_REGISTER_MESH_REFINEMENT_CRITERION macro to register your new class. The implementation of the new class should be in namespace aspect::MeshRefinement.

Specifically, your new class needs to implement the following basic interface:

template <int dim>
    class aspect::MeshRefinement::Interface
    {
      public:
        virtual
        void
        execute (Vector<float> &error_indicators) const = 0;

        static
        void
        declare_parameters (ParameterHandler &prm);

        virtual
        void
        parse_parameters (ParameterHandler &prm);
    };

The first of these functions computes the set of refinement criteria (one per cell) and returns it in the given argument. Typical examples can be found in the existing implementations in the source/mesh_refinement directory. As usual, your termination criterion implementation will likely need to be derived from the SimulatorAccess to get access to the current state of the simulation.

The remaining functions are obvious, and are also discussed in the documentation of this interface class at aspect::MeshRefinement::Interface. The purpose of the last two functions has been discussed in the general overview of plugins above.