Remeshing a function / changing mesh coordinates while preserving function shape

[sorenandflying]

Hi All,

I am working on a project where I need to change the coordinates of a mesh so I am working with a smaller and smaller section of a function.

While I can change mesh coordinates, this ends up "squishing" my function, rather than "cutting" or "zooming" into the smaller section I want to work with.

I can evaluate individual points of a function f_0 using at(), but I need to evaluate a whole sections of f_0 using the same number of cells and the same degree as the original function. I hope my code below makes it a little more clear what I am attempting.

Here is an example of code of some of the variations I've tried so far.

import firedrake
import matplotlib.pyplot as plt
import numpy as np

# Initialize test mesh
Lx_0 = 10
nx = 10
deg = 2

mesh_0 = firedrake.IntervalMesh(nx, Lx_0)
Q_0 = firedrake.FunctionSpace(mesh_0, "CG", deg)

# Define simple function
from firedrake import sin
x_0, = firedrake.SpatialCoordinate(mesh_0)
f_0 = firedrake.interpolate(sin(x_0*3.14159),Q_0);

# Display function
fig, axes = plt.subplots()
firedrake.plot(f_0, axes = axes);

# Define specs of new mesh and function space
Lx_1 = 5
mesh_1 = firedrake.IntervalMesh(nx, Lx_0)
Q_1 = firedrake.FunctionSpace(mesh_1, "CG", deg)

# Interpolating to a new mesh throws an error
f_1 = firedrake.interpolate(f_0, Q_1)

# Evaluating the function at mesh points throws an error
x_2, = firedrake.SpatialCoordinate(mesh_1)
f_2 = firedrake.interpolate(f_0.at(x_2), Q_1)

# Directly altering mesh changes coordinates, but squishes function after interpolation
mesh_0.coordinates.dat.data[:] *= Lx_1/Lx_0
f_2 = firedrake.interpolate(f_0, Q_0)

fig, axes = plt.subplots()
firedrake.plot(f_2, axes = axes);

The result I want looks like the following chart, but I need it to be based on the values of 'f_0`:

Thanks!

[connorjward]

Have you recently run firedrake-update? As of very recently we now support mesh-to-mesh interpolation.