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9.2 Implement our own system assembling

In this tutorial we

• write an integrator for \(\int_T \nabla u \nabla v\)

• put together element matrices to the global system matrix

from ngsolve import *
from ngsolve.webgui import Draw
from netgen.occ import unit_square

from ngsolve.fem import CompilePythonModule
from pathlib import Path

txt = Path('myassemblemodule.cpp').read_text()
m = CompilePythonModule(txt, init_function_name='mymodule', add_header=False)
dir (m)

['MyAssembleMatrix',
 'MyLaplace',
 'MySource',
 '__doc__',
 '__loader__',
 '__name__',
 '__package__',
 '__spec__']

mesh = Mesh(unit_square.GenerateMesh(maxh=0.2))
fes = H1(mesh, order=3, dirichlet=".*")
u, v = fes.TnT()

use our own integrators for element matrix calculation:

a = BilinearForm(fes)
a += m.MyLaplace(CF(1))
a.Assemble()

f = LinearForm(fes)
f += m.MySource(1)
f.Assemble();

gfu = GridFunction(fes)
gfu.vec.data = a.mat.Inverse(fes.FreeDofs()) * f.vec
Draw (gfu);

use our own matrix assembling function:

with TaskManager():
    mymatrix = m.MyAssembleMatrix(fes, m.MyLaplace(CF(1)))
gfu.vec.data = mymatrix.Inverse(fes.FreeDofs()) * f.vec
Draw (gfu);
# print ("my matrix = ", mymat)

We assemble matrix
sequential assembling