Add demo for interpolating expressions (#463)

* Add demo for interpolating expressions

* Revert added comma

* Remove grad expression demo

Author: jorgensd

demo/ExpressionInterpolation.py

@@ -0,0 +1,63 @@
+# Copyright (C) 2022 Jørgen S. Dokken
+#
+# This file is part of FFCx.
+#
+# FFC is free software: you can redistribute it and/or modify
+# it under the terms of the GNU Lesser General Public License as published by
+# the Free Software Foundation, either version 3 of the License, or
+# (at your option) any later version.
+#
+# FFC is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+# GNU Lesser General Public License for more details.
+#
+# You should have received a copy of the GNU Lesser General Public License
+# along with FFC. If not, see <http://www.gnu.org/licenses/>.
+#
+# Defines an Expression which evaluates the several different functions at
+# a set of interpolation points
+
+import basix
+from ufl import (Coefficient, FiniteElement, FunctionSpace, Mesh, MixedElement,
+                 VectorElement, grad, triangle)
+
+# Define mesh
+cell = triangle
+v_el = VectorElement("Lagrange", cell, 1)
+mesh = Mesh(v_el)
+
+# Define mixed function space
+el = FiniteElement("CG", cell, 2)
+el_int = VectorElement("Discontinuous Lagrange", cell, 1)
+me = MixedElement([el, el_int])
+V = FunctionSpace(mesh, me)
+u = Coefficient(V)
+
+# Define expressions on each sub-space
+du0 = grad(u[0])
+du1 = grad(u[1])
+
+# Define an expression using quadrature elements
+q_rule = "gauss_jacobi"
+q_degree = 3
+q_el = FiniteElement("Quadrature", cell, q_degree, quad_scheme=q_rule)
+Q = FunctionSpace(mesh, q_el)
+q = Coefficient(Q)
+powq = 3 * q**2
+
+# Extract basix cell type
+b_cell = basix.cell.string_to_type(cell.cellname())
+
+# Find quadrature points for quadrature element
+b_rule = basix.quadrature.string_to_type(q_rule)
+quadrature_points, _ = basix.make_quadrature(b_rule, b_cell, q_degree)
+
+# Get interpolation points for output space
+family = basix.finite_element.string_to_family("Lagrange", cell.cellname())
+b_element = basix.create_element(family, b_cell, 4, basix.LagrangeVariant.gll_warped, True)
+interpolation_points = b_element.points
+
+# Create expressions that can be used for interpolation
+expressions = [(du0, interpolation_points), (du1, interpolation_points),
+               (powq, quadrature_points)]