# Set Expression values according to gmsh physical regions

**URL:** <https://fenicsproject.discourse.group/t/set-expression-values-according-to-gmsh-physical-regions/13958>\
**Category:** General\
**Tags:** gmsh\
**Created:** [March 18, 2024, 10:22pm UTC](https://fenicsproject.discourse.group/t/set-expression-values-according-to-gmsh-physical-regions/13958 "2024-03-18T22:22:32Z")\
**Posts on this page:** 1\
**Showing post:** 2

<div class="post-metadata">

**Author:** ![Jesus\_Vellojin](https://yyz2.discourse-cdn.com/free1/user_avatar/fenicsproject.discourse.group/jesus_vellojin/32/6485_2.png) [@Jesus\_Vellojin](https://fenicsproject.discourse.group/u/Jesus_Vellojin)\
**Post date:** [March 19, 2024, 12:12am UTC](https://fenicsproject.discourse.group/t/set-expression-values-according-to-gmsh-physical-regions/13958/2 "2024-03-19T00:12:14Z")

</div>

Hi, welcome to the FEniCS community!

It is pretty hard to guess what you would like to achieve without a MWE. I recommend you to read [https://fenicsproject.discourse.group/t/read-before-posting-how-do-i-get-my-question-answered/21](https://fenicsproject.discourse.group/t/read-before-posting-how-do-i-get-my-question-answered/21).

Assuming that you import the tags:

```auto
mesh = Mesh("MSL_XY.xml")
subdomains = MeshFunction("size_t", mesh, "MSL_XY_physical_region.xml")
boundaries = MeshFunction("size_t", mesh, "MSL_XY_facet_region.xml")

```

and redefine the measures as

```auto
dx = Measure('dx', domain=mesh, subdomain_data= subdomains)
ds = Measure('ds', domain=mesh, subdomain_data=boundaries)
dS = Measure('dS', domain=mesh, subdomain_data=boundaries)

```

Then you can use this to define your expression for each subdomain, i.e.,

```auto
def eps1(u):
    return 0.5*(grad(u) + grad(u).T)

def eps2(u):
    return 0.6*(grad(u) + grad(u).T)

I1 = inner(eps1(u),eps1(v))*dx(1)
I2 = inner(eps2(u),eps2(v))*dx(2)

```

where `dx(1)` and `dx(2)` are the volumetric measures for subdomains tagged as 1 and 2, respectively. Similarly for `ds` and `dS`.

You could also define a custom expression:

```auto
class Mu(UserExpression):
    """
    This class defines a variable mu that takes different values
    on the unitsquare domain (0,1)^2 at x<0.5 and x>0.5. The mesh is 
    assumed to be conforming in x=0.5
    """

    def __init__ (self, p1, p2, **kwargs):
        super(). __init__ (**kwargs)
        self.p1 = p1
        self.p2 = p2

    def eval(self, value, x):
        if x[0] < 0.5. + DOLFIN_EPS:
            value[0] = self.p1(x)
        else:
            value[0] = self.p2(x)

    def value_shape(self):
            return ()

p1 = Expression('x[1]', degree=1)
p2 = Expression('x[0]+x[1]', degree=1)

mu = Mu(p1, p2, degree=2)

```

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_[View the full topic](https://fenicsproject.discourse.group/t/set-expression-values-according-to-gmsh-physical-regions/13958)._