Elementwise Minimum of a Function

Question

Hello,

I'm trying to compute the element wise minimum of a function, that is I need a P_0 function which is smaller than the original function.

mesh = UnitSquareMesh( 10, 10 )
space = FunctionSpace( mesh, "CG", 1 )
spaceP0 = FunctionSpace( mesh, "DG", 0 )
fun = interpolate( Expression( "sin( x[0] * pi ) * sin( x[1] * pi )" ), space )
funP0 = Function( spaceP0 )
# compute values of funP0 such that funP0 <= fun

Has anybody an idea how to do this fast and high level?

Thanks in advance,
Jo

Comments

right now i'm using something like this as a workaround:

mesh = UnitSquareMesh( 3, 3 )
space = FunctionSpace( mesh, "CG", 1 )
space0 = FunctionSpace( mesh, "DG", 0 )
fun = interpolate( Expression( "sin( x[0] * pi ) * sin( x[1] * pi )" ), space )

funVals = fun.vector().array()
vert2dofP1 = vertex_to_dof_map( space )
vertVals = funVals[vert2dofP1]

cells = mesh.cells()
cellVals = vertVals[ cells ]
minVals = numpy.min( cellVals, 1 )

funMin = Function( space0 )
funMin.vector()[:] = minVals

plot( funMin )
interactive()

The problem is, that this only works for P1 and not for Pk (no dof map as dofs are not on vertices). Furthermore this assumes the ordering of the P0 dofs (again no dof map).

Answer 1

Hi, here's a way to solve your problem using dofmaps

from dolfin import *

mesh = UnitSquareMesh(20, 20)
space = FunctionSpace(mesh, "CG", 4)
space0 = FunctionSpace(mesh, "DG", 0)

fun = interpolate(Expression("sin(4*x[0]*pi)*sin(4*x[1]* pi)"), space)
fun0 = Function(space0)

vec = fun.vector()
vec0 = fun0.vector()

dofmap = space.dofmap()
dofmap0 = space0.dofmap()

for cell in cells(mesh):
    i = cell.index()
    vec0[dofmap0.cell_dofs(i)] = vec[dofmap.cell_dofs(i)].min()

plot(fun, interactive=True)
plot(fun0, interactive=True)

Comments

Thanks! This works like a charm. And now I have learned how to properly use dofmaps!