Hello,
I have a question about how dolfin assembles a stiffness matrix over a subdomain.
I am timing the assembly of a stiffness matrix on a mesh that has 2800 elements.
Then I define a subdomain on that mesh, with only 10 elements.
I time the assembly of the same matrix form over the 10 element subdomain.
It is only about 7 times faster than the full assembly, even though it should only have to loop through 10 cells.
Does somebody know why that is?
Thank you
As you have not supplied any code, it is hard to pinpoint why this is the case for you.
I think one thing your are not taking into account is the setup cost of the sparse matrices.
See the following example which illustrates run-times where you only iterate over a small sub-set of your mesh.
from dolfin import *
N = 400
frac = 0.02
mesh = UnitSquareMesh(N, N)
V = FunctionSpace(mesh, "CG", 1)
class domain(SubDomain):
def inside(self, x, on_boundary):
return x[0]< frac
mf = MeshFunction("size_t", mesh, mesh.topology().dim(), 0)
domain().mark(mf, 1)
dx_c = Measure("dx", domain=mesh, subdomain_data=mf)
u = TrialFunction(V)
v = TestFunction(V)
a = inner(grad(u), grad(v))*dx_c
a_form = Form(a)
A = assemble(a_form)
a_sub = inner(grad(u), grad(v))*dx_c(1)
a_sub_form = Form(a_sub)
A_sub = assemble(a_sub_form)
import timeit
runs = 100
full = timeit.timeit(lambda: assemble(a_form, tensor=A), number=runs)
sub = timeit.timeit(lambda: assemble(a_sub_form, tensor=A_sub), number=runs)
print(sub/full, frac, sub, frac)
For this example, this returns:
0.028362406769913293 0.02 0.20799705399986124 0.02
If you reduce the fraction even further, for instance to (0.001) you will observe that we do not get optimal performance any longer, as we get:
0.01412187111184388 0.001 0.1051290079994942 0.001
This is because there are certain costs associated with assembling a matrix. Assembling over only 10 cells is very little, and the setup cost is dominating the run-time.