def mesh():
geo = SplineGeometry()
geo.AddRectangle( (-10, 0.0), (10, 1), leftdomain=1, bcs=["bottom","right","slave","left"])
geo.AddCircle ( (-1, 5), r=1, leftdomain=2, bc="master")
geo.SetMaterial(1, "brick")
geo.SetMaterial(2, "ball")
mesh = Mesh( geo.GenerateMesh(maxh=0.5))
mesh.Curve(5)
Draw(mesh)
return mesh
from netgen.geom2d import SplineGeometry from ngsolve import * geo = SplineGeometry() geo.AddCircle( (0,0), 1.4, leftdomain=2) geo.AddCircle( (0,0), 1, leftdomain=1, rightdomain=2) geo.SetMaterial(1, "inner") geo.SetMaterial(2, "pml") mesh = Mesh(geo.GenerateMesh (maxh=0.1)) mesh.SetPML(pml.Radial(rad=1,alpha=1j,origin=(0,0)), "pml") fes = H1(mesh, order=4, complex=True) u = fes.TrialFunction() v = fes.TestFunction() omega = 10 a = BilinearForm(fes) a += SymbolicBFI(grad(u)*grad(v)-omega*omega*u*v) f = LinearForm(fes) f += SymbolicLFI(exp(-20**2*((x-0.3)*(x-0.3)+y*y))*v) a.Assemble() f.Assemble() gfu = GridFunction(fes) gfu.vec.data = a.mat.Inverse() * f.vec Draw(gfu)
geo = SplineGeometry()
p1, p2, p3, p4 = [
geo.AppendPoint(x, y) for x, y in [(0, 0), (1, 0), (1, 1), (0, 1)]
]
p5, p6 = [geo.AppendPoint(x, y) for x, y in [(2, 0), (2, 1)]]
geo.Append(["line", p1, p2], leftdomain=1, rightdomain=0, bc='outer')
geo.Append(["line", p2, p3], leftdomain=1, rightdomain=2, bc='interface')
geo.Append(["line", p3, p4], leftdomain=1, rightdomain=0, bc='outer')
geo.Append(["line", p4, p1], leftdomain=1, rightdomain=0, bc='outer')
geo.Append(["line", p2, p5], leftdomain=2, rightdomain=0, bc='outer')
geo.Append(["line", p5, p6], leftdomain=2, rightdomain=0, bc='outer')
geo.Append(["line", p6, p3], leftdomain=2, rightdomain=0, bc='outer')
geo.SetMaterial(1, 'left')
geo.SetMaterial(2, 'right')
mesh = Mesh(geo.GenerateMesh(maxh=0.1))
Draw(mesh)
order = 3
Vl = H1(mesh, order=order, definedon="left")
Vr = H1(mesh, order=order, definedon="right")
Q = SurfaceL2(mesh, order=order - 1)
X = FESpace([Vl, Vr, Q])
a = BilinearForm(X)
f = LinearForm(X)
from time import time_ns
print("Welcome, Peter!")
### Definition of mesh ###
h = 0.5
geo = SplineGeometry()
geo.AddRectangle((0, 0), (1, 1),
bcs=['b', 'r', 't', 'l'],
leftdomain=1,
rightdomain=0)
geo.AddRectangle((0.3, 0.5), (0.5, 0.7),
bcs=['b1', 'r1', 't1', 'l1'],
leftdomain=2,
rightdomain=1)
geo.SetMaterial(1, "d2")
geo.SetMaterial(2, "d1")
mesh = Mesh(geo.GenerateMesh(maxh=h)) # standard mesh available
print('#' * 40)
print("Mesh generated:")
print('#' * 40)
print("Number of vertices: ", mesh.nv)
print("Number of elements: ", mesh.ne)
print("Dimension of mesh: ", mesh.dim)
lams = {"d1": 1, "d2": 10}
Lambda = CoefficientFunction([lams[mat] for mat in mesh.GetMaterials()])
cs = {"d1": 1, "d2": 0}
C = CoefficientFunction([cs[mat] for mat in mesh.GetMaterials()])
Draw(mesh)
### Definition of FES ###
# pylint: disable=unused-wildcard-import
import netgen.gui
from ngsolve import *
from netgen.geom2d import SplineGeometry
print("Welcome, Peter!")
### Definition of mesh ###
h = 0.1
geo = SplineGeometry()
geo.AddRectangle((0, 0), (1, 1),
bcs=['b', 'r', 't', 'l'],
leftdomain=1,
rightdomain=0)
geo.SetMaterial(1, "D")
mesh = Mesh(geo.GenerateMesh(maxh=h)) # standard mesh available
print('#' * 40)
print("Mesh generated:")
print('#' * 40)
print("Number of vertices: ", mesh.nv)
print("Number of elements: ", mesh.ne)
print("Dimension of mesh: ", mesh.dim)
Draw(mesh)
### Definition of FES ###
# define discrete conforming spaces of Sigma and V
# any idea why we need a different order here?
# try to use different combinations later as well
# a)
get_ipython().run_line_magic('matplotlib', 'notebook')
import netgen.gui
from netgen.geom2d import SplineGeometry
from ngsolve import *
import matplotlib.pyplot as plt
import numpy as np
# We can model the problem as a set of concentric circles with the center most being our region of interest, $\Omega$. This is then sourrounded by a 'normal' region and then a PLM region.
# In[2]:
geo = SplineGeometry()
geo.AddCircle((0, 0), 2.25, leftdomain=3, bc="outerbnd")
geo.AddCircle((0, 0), 1.75, leftdomain=2, rightdomain=3, bc="midbnd")
geo.AddCircle((0, 0), 1, leftdomain=1, rightdomain=2, bc="innerbnd")
geo.SetMaterial(1, "inner")
geo.SetMaterial(2, "mid")
geo.SetMaterial(3, "pmlregion")
mesh = Mesh(geo.GenerateMesh(maxh=0.1))
mesh.Curve(3)
mesh.SetPML(pml.Radial(rad=1.75, alpha=1j, origin=(0, 0)),
"pmlregion") #Alpha is the strenth of the PML.
# We can set
#
# $$c(x) = \begin{cases}
# 1 &\text{: } x\in\mathbb{R}^2/\Omega \\
# 100 &\text{: } x\in\Omega
# \end{cases}$$
#
# -*- coding: utf-8 -*-
# Example for generating a simple netgen mesh
from ngsolve import *
from netgen.geom2d import SplineGeometry
geo = SplineGeometry()
p1,p12a,p12b,p2,p3,p4 = [ geo.AppendPoint(x,y) for x,y in [(-5,5),(-5,2),(-5, -2),(-5,-5),(5,-5),(5,5)] ]
geo.SetMaterial(1, "background")
geo.SetMaterial(2, "circles")
# In NetGen, regions are defined using 'left' and 'right',
# For example, leftdomain=2, rightdomain=1 means when moving from a
# from a point A to B, region 2 is always on the left side and
# region 1 is on the right.
geo.Append (["line", p1, p12a], leftdomain=1, bc="boundary1")
geo.Append (["line", p12a, p12b], leftdomain=1, bc="lightsource")
geo.Append (["line", p12b, p2], leftdomain=1, bc="boundary1")
geo.Append (["line", p2, p3], leftdomain=1, bc="boundary1")
geo.Append (["line", p3, p4], leftdomain=1, bc="boundary1")
geo.Append (["line", p4, p1], leftdomain=1, bc="boundary1")
geo.AddCircle(c=(1,1), r=1, leftdomain=2,rightdomain=1)
geo.AddCircle(c=(-2,-2), r=2, leftdomain=2,rightdomain=1)
mesh = geo.GenerateMesh(maxh=0.1)
mesh.Save("square_with_two_circles.vol")
