My CoefficientFunction

Creating your own CoefficientFunctions is probably the most common thing someone needs to do when you have to dive into NGSolve C++. There's a lot you can do from Python, but sometimes you want something special that's not possible. This tutorial shows how to create arbitrary CoeffientFunctions.

For it's basic functionality a CF does not need much: Derive from the base class, provide a constructor and override the pure virtual method Evaluate. The CF in our example will just return x*y.

A simple implementation of the CF would look like this:

namespace ngfem
{
  class MyCoefficientFunction : public CoefficientFunction
  {
  public:
    MyCoefficientFunction()
      : CoefficientFunction(/*dimension = */ 1) { ; }

    // ********************* Necessary **********************************
    virtual double Evaluate(const BaseMappedIntegrationPoint& mip) const override
    {
      // maybe do something with mip and trafo?
      auto pnt = mip.GetPoint();
      return pnt[0] * pnt[1];
    }

  };
}

Note that there are a lot of other virtual functions a CF can override, mostly for performance (i.e. evaluate in all IntegrationPoints of an IntegrationRule at once or use AVX vectorization with our SIMD class), but we want to keep it simple for now.

Next we want to make our CF accessible from Python. Therefore we use pybind11 to export the class by createing a py::class_ instance. This template class takes the exported class, then the holder type (a shared pointer to the exported class) and the base class(es) as template arguments. The constructor takes the module where we export it, it's Python name and the docstring. Further we define an __init__ function, where we use the default pybind py::init method, which just calls the class constructor with the same arguments we give as template arguments. Note that the semicolon is in the next line: .def always returns the object again, so we can use it to define multiple functions for the class and then after all definitions close the statment with the semicolon.

    py::class_<MyCoefficientFunction, shared_ptr<MyCoefficientFunction>, CoefficientFunction>
      (m, "MyCoefficient", "CoefficientFunction that returns x*y.")
      .def(py::init<>())

To be able to pickle and unpickle your CoefficientFunction you need to register it to the NGSolve archiver. This is done by creating a static object of the template class RegisterClassForArchive<Class, Baseclass>:

  static RegisterClassForArchive<MyCoefficientFunction, CoefficientFunction> regmycf;

The next step will be to create a new finite element.