Add function decorator for weakforms

[adtzlr]

introduce a new function decorator @Form():

import numpy as np
from felupe.math import ddot
import felupe as fem

mesh = fem.mesh.triangulate(fem.Rectangle(n=6))
region = fem.RegionTriangle(mesh)
field = fem.Field(region)
coords = fem.Field(
    region, dim=mesh.dim, values=mesh.points
).interpolate()

@fem.Form(v=field, u=field, grad_v=True, grad_u=True)
def a(dv, du):
    return ddot(dv, du)

@fem.Form(v=field)
def L(v, coords):
    x, y = coords
    f = np.sin(np.pi * x) * np.sin(np.pi * y)
    return f * v

L.assemble(v=field, kwargs={"coords": coords})
a.assemble(v=field, u=field)

fixes #207

[codecov-commenter]

Codecov Report

Merging #208 (3b6fe1d) into main (9b2c1d8) will increase coverage by 0.00%.
The diff coverage is 98.63%.

@@           Coverage Diff           @@
##             main     #208   +/-   ##
=======================================
  Coverage   98.34%   98.35%           
=======================================
  Files          62       62           
  Lines        2543     2608   +65     
=======================================
+ Hits         2501     2565   +64     
- Misses         42       43    +1     

Impacted Files	Coverage Δ
felupe/__init__.py	92.00% <ø> (ø)
felupe/_assembly/_base.py	93.50% <ø> (ø)
felupe/_field/_axi.py	95.45% <ø> (ø)
felupe/_field/_base.py	92.30% <ø> (ø)
felupe/element/_triangle.py	100.00% <ø> (ø)
felupe/tools/_save.py	100.00% <ø> (ø)
felupe/_assembly/_form.py	99.46% <98.46%> (-0.54%)	⬇️
felupe/_assembly/__init__.py	100.00% <100.00%> (ø)
felupe/math/__init__.py	100.00% <100.00%> (ø)
felupe/mesh/_convert.py	96.39% <100.00%> (ø)
... and 2 more

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[adtzlr]

Mixed-Field implementation is still broken as LinearFormMixed and BilinearFormMixed expect a list of weakforms. This can't be decorated. A new decorator has to be introduced...

[adtzlr]

Mixed-Field Forms are applied on a helper function which returns a list of sub-forms (upper triangle part).

mesh = fe.Cube(n=3)
region = fe.RegionHexahedron(mesh)
fieldmixed = fe.FieldsMixed(region, n=2)
F, p = fieldmixed.extract()

def a_uu(v, u, F, p):
    return ddot(u, ddot(dya(F, F), v))

def a_up(v, r, F, p):
    return dot(p, r) * ddot(F, v)

def a_pp(q, r, F, p):
    return dot(p, q) * dot(r, p)

@fe.Form(v=fieldmixed, u=fieldmixed, grad_v=(True, False), grad_u=(True, False))
def a():
    return (a_uu, a_up, a_pp)

a.assemble(v=fieldmixed, u=fieldmixed, args=(F, p))