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Implement our own system assembling

23. Implement our own system assembling#

In this tutorial we

  • write integrators for \(\int_T f v dx\) and \(\int_T \nabla u \nabla v dx\):

  • put together element matrices to the global system matrix:

The implementation is available on github: TUWien-ASC/NGS-myassembling

from ngsolve import *
from ngsolve.webgui import Draw
import myassembling
dir (myassembling)

Loading myassembling library

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

mesh = Mesh(unit_square.GenerateMesh(maxh=0.2))
fes = H1(mesh, order=2, dirichlet=".*")
u, v = fes.TnT()

23.1. use our own integrators for element matrix calculation:#

a = BilinearForm(fes)
a += myassembling.MyLaplace(1)
a.Assemble()

f = LinearForm(fes)
f += myassembling.MySource(x)
f.Assemble();

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

23.2. we can inspect the element matrix:#

mylap = myassembling.MyLaplace(1)
ei = ElementId(VOL,17)
mylap.CalcElementMatrix(fes.GetFE(ei), mesh.GetTrafo(ei))

 0.665986 -0.426433 -0.239553 -0.0710721 0.110998 -0.0399256
 -0.426433 0.648429 -0.221997 0.108072 -0.0710721 -0.0369995
 -0.239553 -0.221997 0.46155 -0.0369995 -0.0399256 0.076925
 -0.0710721 0.108072 -0.0369995 0.0369993 -0.017768 -0.00924986
 0.110998 -0.0710721 -0.0399256 -0.017768 0.0369993 -0.00998139
 -0.0399256 -0.0369995 0.076925 -0.00924986 -0.00998139 0.0369993

23.3. use our own matrix assembling function:#

for l in range(4): mesh.Refine()
fes.Update()
gfu.Update()
f.Assemble();

mymatrix = myassembling.MyAssembleMatrix(fes, myassembling.MyLaplace(CF(1)))
# mymatrix = myassembling.MyAssembleMatrix(fes, (grad(u)*grad(v)*dx)[0].MakeBFI())

if fes.ndof < 100000:
    gfu.vec.data = mymatrix.Inverse(fes.FreeDofs()) * f.vec
    Draw (gfu);

We assemble matrix

23.4. Exercise:#

  • Implement MyAssembleVector for building the right hand side vector for \(\int_\Omega f v \, dx\)

  • Implement MyNeumannIntegrator for evaluating \(\int_{\partial \Omega} g v \, ds\)

  • Have a look into thread-parallel assembling at NGSolve-itutorials unit 9.2

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