I am trying to solve an electrostatic poissons equation with 2 different materials. I am trying to compute the electric potential for a sphere (ϵr= 10) embedded inside a box (ϵr= 1).
I am getting the below error at the affineFEoperator step:
julia> op = AffineFEOperator(a,b,U,V)
ERROR: promotion of types VectorValue{3, Float64} and Int64 failed to change any arguments
I am using the below code:
using Gridap, GridapGmsh, Gridap.Fields, Gridap.Geometry
const epsr_box = 1.0 ; # Relative electric permittivity for box
const epsr_sphere = 10.0 ; # Relative electric permittivity for sphere
model = GmshDiscreteModel("box_sph.msh"); # geometry contains a sphere domain and a box excluding the sphere i.e.. box-sphere
order = 1;
reffe = ReferenceFE(lagrangian,Float64,order);
V = TestFESpace(model,reffe,dirichlet_tags = ["HVelec", "GNDelec"]);
U = TrialFESpace(V, [2.0, 0.0]); # apply voltage at the two opposite faces of the box
degree = 1;
Ω = Triangulation(model);
dΩ = Measure(Ω,degree);
labels = get_face_labeling(model);
dimension = num_cell_dims(model);
tags = get_face_tag(labels,dimension); # get all the tags in the geometry
const sphere_tag = get_tag_from_name(labels,"sphere"); # get tag of sphere geometry
const box_tag = get_tag_from_name(labels,"box"); # get tag of box geometry
function epsr(tag)
if tag == box_tag
return epsr_box
elseif tag == sphere_tag
return epsr_sphere
end
end
a(u,v) = ∫( (∇(v)).(epsr*(∇(u))) )dΩ
f(x)=0.0; # assume laplace equation for now and later to have f as f(x,y,z)
b(v) = ∫(v*f)dΩ ;
op = AffineFEOperator(a,b,U,V)
uh = solve(op)
Welcome Balaji, Please read this topic to make it easier to help you. Please edit you post and write your julia code within quoted code.
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(I edited the post to quote the code.)
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This doesn’t look right. The dot product operator is ⋅ (unicode dot operator, which can be typed with \cdot<TAB> at the julia> prompt or in editors with appropriate plugins), not . (period). A dot product can also be written dot(∇(v), epsr*(∇(u))) without the Unicode operator, but Gridap’s API is pretty Unicode-heavy in general.
See also the Gridap Poisson tutorial.
Also, I think you need to tell it to pass the tags to epsr more explicitly here. See e.g. how the tags are passed in the Gridap linear elasticity example. I think that is the source of your error message — from the way you are using it, Gridap thinks that epsr must be a function epsr(x) of the position vector x, which causes an error because epsr expects an integer tag argument.
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Thank you very much. I am relatively new to julia programming. I modified the original code using the dot() operator instead of “.” as you suggested .I am writing the modified section of the new code below.
function epsr(tag)
if tag == box_tag
return epsr_box
elseif tag == sphere_tag
return epsr_sphere
end
end
a(u,v) = ∫( dot(∇(v) , (epsr∘(∇(u),tags))) )*dΩ
I am getting a different error but at the same step as before:
julia> op = AffineFEOperator(a,b,U,V)
ERROR: MethodError: no method matching epsr(::VectorValue{3, Float64}, ::Int8)
Closest candidates are:
epsr(::Any)
Also, I went through the documentation on multi-material elasticity modeling: 3 Linear elasticity · Gridap tutorials. I am still unclear on the syntax part. because, in the example problem the function σ_bimat has arguments (ε,tag) of which ε is itself an operator defined by 1/2(∇u+(∇u) '). Whereas in my case, the function epsr has only tag as the argument, so how can I write the weak form.
I request you to help me with 2 things.
- The correct modification of the code.
- Any link or documentation or youtube material that will help me learn the syntax of these operators/functions (as I am a beginner).
That’s because your epsr function should now take ∇(u) as the first argument since you are composing it with (∇(u),tags), e.g.
function epsr(∇u, tag)
if tag == box_tag
return epsr_box * ∇u
elseif tag == sphere_tag
return epsr_sphere * ∇u
end
end
(similar to the tutorial I linked),
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