Add FEniCSx solver for partitioned heat conduction tutorial

changelog-entries/687.md

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+- Added FEniCSx solver for the partitioned heat conduction tutorial following the [FEniCS solver](https://github.com/precice/tutorials/tree/develop/partitioned-heat-conduction/solver-fenics)

partitioned-heat-conduction/dirichlet-fenicsx/precice-adapter-config-D.json

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+{
+  "participant_name": "Dirichlet",
+  "precice_config_file_path": "../precice-config.xml",
+  "interfaces": [
+    {
+      "mesh_name": "Dirichlet-Mesh",
+      "write_data": [
+        {
+          "name": "Heat-Flux"
+        }
+      ],
+      "read_data": [
+        {
+          "name": "Temperature"
+        }
+      ]
+    }
+  ]
+}

partitioned-heat-conduction/dirichlet-fenicsx/run.sh

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+#!/bin/sh
+set -e -u
+
+python3 -m venv --system-site-packages .venv
+. .venv/bin/activate
+pip install -r ../solver-fenicsx/requirements.txt
+
+python3 ../solver-fenicsx/heat.py Dirichlet

partitioned-heat-conduction/neumann-fenicsx/precice-adapter-config-N.json

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+{
+  "participant_name": "Neumann",
+  "precice_config_file_path": "../precice-config.xml",
+  "interfaces": [
+    {
+      "mesh_name": "Neumann-Mesh",
+      "write_data": [
+        {
+          "name": "Temperature"
+        }
+      ],
+      "read_data": [
+        {
+          "name": "Heat-Flux"
+        }
+      ]
+    }
+  ]
+}

partitioned-heat-conduction/neumann-fenicsx/run.sh

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+#!/bin/sh
+set -e -u
+
+python3 -m venv --system-site-packages .venv
+. .venv/bin/activate
+pip install -r ../solver-fenicsx/requirements.txt
+python3 ../solver-fenicsx/heat.py Neumann

partitioned-heat-conduction/solver-fenicsx/clean.sh

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+#!/bin/sh
+set -e -u
+
+. ../../tools/cleaning-tools.sh
+
+clean_fenics .

partitioned-heat-conduction/solver-fenicsx/errorcomputation.py

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+from dolfinx import fem
+import numpy as np
+from mpi4py import MPI
+import ufl
+
+
+def compute_errors(u_approx, u_ref, total_error_tol=10 ** -9):
+    mesh = u_ref.function_space.mesh
+    # Compute L2 error and error at nodes
+    error_L2 = np.sqrt(mesh.comm.allreduce(fem.assemble_scalar(fem.form((u_approx - u_ref)**2 * ufl.dx)), op=MPI.SUM))
+    if mesh.comm.rank == 0:
+        print(f"L2-error: {error_L2:.2e}")
+
+    # Compute values at mesh vertices
+    error_max = mesh.comm.allreduce(np.max(np.abs(u_approx.x.array - u_ref.x.array)), op=MPI.MAX)
+    if mesh.comm.rank == 0:
+        print(f"Error_max: {error_max:.2e}")
+
+    assert (error_L2 < total_error_tol)
+
+    return (error_L2, error_max)