Fast cell-based material allocation

NGSolve
1

Hey all,

I am modeling a highly inhomogeneous 3D problem and therefore need a fast cell-based material allocation.

The material is stored in cell_material, where cell_material[j] corresponds to the material in cell j. Is it possible to create a coefficient function that is used in the bilinear form with the following mapping property:

coefficient function: index of the currently integrated cell ā†’ material parameter within this cell ?

There is an alternative that uses an auxiliary finite element space with constant basis function to assign the material to each cell, but Iā€™m not convinced of its speed:

material_fes = L2(mesh, order=0) # constant function in every cell
material_gf = GridFunction(material_fes)

for el in mesh.Elements():
    j = el.nr
    material_gf.vec.data[j] = cell_material[j]

material_cf = CoefficientFunction(material_gf).Compile()

The approach I asked for should be much faster than the example I gave before. Maybe someone has information about what possibilities ngsolve offers.

I am very grateful for help.

2

you can skip the python loop

material_gf.vec.FV().NumPy()[:] = cell_material

if cell_material is a numpy array. But what should be faster than this?

3

Thank you for your answer. You are right with your point, but I meant the speed of assembly of the system matrix.

If the cell material is known from the index of the cell it should be much faster compared to a coefficient function that is defined based on a grid function. Let me explain this in detail:

I assume that the evaluation of a grid function at a certain point in space requires two steps:

  1. Find the cell that contains the point of interest
  2. Evaluate the function value inside this cell at the point of interest

I would like to know if there is an option to avoid the first step, by using a special coefficient function that only uses the cell index of the currently integrated cell and maps it to the material defined inside this cell.

4

The gridfunction doesnt need to find the element. The fespace knows which dofs are associated with which elements.
Integrate/assemble loops over elements and this info is used.
Best Christopher

1 Like
5

Thank you very much for the information,

I have found out that it is not the system matrix that takes so long to set up, but my preconditioner.