Advanced expression manipulation¶

In this section, we shall present different different features for manipulating expressions such us finding the Kronecker representation for bilinear forms.

Tensorization¶

Assume we have the following bilinear form for Laplace

from sympde import grad, dot
from sympde import FunctionSpace
from sympde import TestFunction
from sympde import BilinearForm
from sympde.core import tensorize

V = FunctionSpace('V', ldim=2)
U = FunctionSpace('U', ldim=2)

v = TestFunction(V, name='v')
u = TestFunction(U, name='u')

a = BilinearForm((v,u), dot(grad(v), grad(u)) + v*u)
print(tensorize(a))

the result is then

>>> Mass(v1,u1)xMass(v0,u0) + Mass(v1,u1)xStiffness(v0,u0) + Stiffness(v1,u1)xMass(v0,u0)

which is what we expect, when splitting the integrals with respect to the two directions. Printing the corresponding latex code gives

${\int_{0}^{1} u_{1} v_{1} dy}\otimes {\int_{0}^{1} u_{0} v_{0} dx} + {\int_{0}^{1} u_{1} v_{1} dy}\otimes {\int_{0}^{1} u_{0}^\prime v_{0}^\prime dx} + {\int_{0}^{1} u_{1}^\prime v_{1}^\prime dy}\otimes {\int_{0}^{1} u_{0} v_{0} dx}$