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ensure boundary condition during adaptive mesh refinement

nsc
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4 years 2 weeks ago #2568 by nsc

ensure boundary condition during adaptive mesh refinement was created by nsc

Hi,

as the title suggests, I would like to make sure, that the inhomogeneous boundary conditions are preserved during the adaptive mesh refinement scheme. In my current program, the first solution looks correct. However, after the error estimation and the refinement, the solution is 0 (or near 0) on the boundary. I think that the error estimation function is not correct, but I am struggling to find my blunder.

The PDE to be solved is:

[tex]-\Delta u(x) = -(18x^2-6)e^{-1.5(x^2 + y^2)}-(18y^2-6)e^{-1.5(x^2 + y^2)}[/tex]
on the domain
[tex]\Omega: x,y \in [-1,1][/tex]
subjected to the boundary condition
[tex]u(x,y)|_{\partial \Omega} = 2e^{-1.5(x^2 + y^2)}[/tex]

Code:

import netgen.gui
from ngsolve import *
import netgen.geom2d as geom2d

geo = geom2d.SplineGeometry()
geo.AddRectangle((-1,-1), (1,1), bcs=["bottom", "right", "top", "left"])
mesh = Mesh(geo.GenerateMesh(maxh=0.05))
mesh.GetBoundaries()

fes = H1(mesh, order=2, dirichlet="left|right|top|bottom")

g = 2*exp(-1.5*(x**2 + y**2))

gfu = GridFunction(fes)
gfu.Set(g, definedon=mesh.Boundaries("left|right|top|bottom"))
Draw(gfu)

u, v = fes.TnT()
a = BilinearForm(fes)
a += grad(u)*grad(v)*dx
f = LinearForm(fes)
f += (-(18*x*x-6)*exp(-1.5*(x*x + y*y))-(18*y*y-6)*exp(-1.5*(x*x + y*y)))*v*dx
c = Preconditioner(a,"multigrid")

space_flux = HDiv(mesh, order=2)
gf_flux = GridFunction(space_flux, "flux")

def solveStep():
    fes.Update()
    gfu.Update()
    Draw(gfu)
    a.Assemble()
    f.Assemble()
    solvers.BVP(bf=a, lf=f, gf=gfu, pre=c)
    gfu.Update()
    Redraw(blocking=True)

def estimateError():
    space_flux.Update()
    gf_flux.Update()
    flux = grad(gfu)
    gf_flux.Set(flux) 
    
    err = (flux-gf_flux)*(flux-gf_flux)
    Draw(err, mesh, 'error_representation')
    eta2 = Integrate(err, mesh, VOL, element_wise=True)
    
    maxerr = max(eta2)
    for el in mesh.Elements():
        mesh.SetRefinementFlag(el, eta2[el.nr] > 0.25*maxerr)

solveStep()

estimateError()

mesh.Refine()

solveStep()

Draw(gfu)

Attachments:

...e_and_bc.ipynb

mneunteufel
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4 years 2 weeks ago #2570 by mneunteufel

Replied by mneunteufel on topic ensure boundary condition during adaptive mesh refinement

Hi nsc,

when the GridFunction is updated, the set Dirichlet boundary data is forgotten. You need to set the data again in your solveStep function

Code:

gfu.Set(g, definedon=mesh.Boundaries("left|right|top|bottom")).

You can use the autoupdate flag for FESpaces and GridFunctions. Then you do not need to call the Update method by hand, see attached file.

File Attachment:

File Name: adaptive_and_bc.py
File Size:1 KB

Best,
Michael

Attachments:

adaptive_and_bc.py

The following user(s) said Thank You: nsc

nsc
Topic Author
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4 years 2 weeks ago #2571 by nsc

Replied by nsc on topic ensure boundary condition during adaptive mesh refinement

Thank you so much for your help! It works perfectly fine now.
I can't believe that I have wasted so much time on such a simple problem.

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