Field normalisation

Apart from setting the value of a field, it is sometimes necessary to normalise it to a certain value. Also sometimes in the case of vector fields, it is required to set the value of certain points in the mesh to be zero. This can be achieved using discretisedfield.Field.norm.

import discretisedfield as df

p1 = (-50, -50, -50)
p2 = (50, 50, 50)
cell = (5, 5, 5)
mesh = df.Mesh(p1=p1, p2=p2, cell=cell)

value = (1, 1, 1)
field = df.Field(mesh, nvdim=3, value=value)

Asking for a norm of the field returns a scalar field with norm values.

field.norm

Field

• Mesh
  • Region
    • pmin = [-50, -50, -50]
    • pmax = [50, 50, 50]
    • dims = ['x', 'y', 'z']
    • units = ['m', 'm', 'm']
  • n = [20, 20, 20]
• nvdim = 1

field.nvdim

3

field.norm(field.mesh.region.random_point())

/tmp/ipykernel_24263/4270432668.py:1: DeprecationWarning: This method will be removed and should not be used anymore.
  field.norm(field.mesh.region.random_point())

array([1.73205081])

If we want to normalise the field with a new value, we write

field.norm = 1

The new value of the field is

field(field.mesh.region.random_point())

/tmp/ipykernel_24263/1582582780.py:1: DeprecationWarning: This method will be removed and should not be used anymore.
  field(field.mesh.region.random_point())

array([0.57735027, 0.57735027, 0.57735027])

and the norm is

field.norm(field.mesh.region.random_point())

/tmp/ipykernel_24263/4270432668.py:1: DeprecationWarning: This method will be removed and should not be used anymore.
  field.norm(field.mesh.region.random_point())

array([1.])

If we now change the value of the field, the norm is not valid anymore

field.update_field_values((-1, -1, 10))
field.norm(field.mesh.region.random_point())

/tmp/ipykernel_24263/4282347518.py:2: DeprecationWarning: This method will be removed and should not be used anymore.
  field.norm(field.mesh.region.random_point())

array([10.09950494])

Instead of a constant, a Pyhton function or another field object can be used to set up the norm. Let us say we want to define a sphere inside the mesh of radius 50. This means that the norm of the field outside the sphere is zero and inside it is 1.

def norm_function(pos):
    x, y, z = pos
    if x**2 + y**2 + z**2 <= 50**2:
        return 1
    else:
        return 0


sphere_field = df.Field(mesh, nvdim=3, value=(10, 0, 0), norm=norm_function)

If we sample the value of the field outside the sphere we get

sphere_field((-50, -50, -50))

array([0., 0., 0.])

sphere_field((0, 0, 0))

array([1., 0., 0.])